Yes, the Resistance sent Kyle to 1984 using the same Time Displacement Equipment (TDE) that Skynet used to send the T-800 from the first film to 1984.
DR. SILBERMAN: "Is that when you captured the lab complex and found that, uh, what is it called, uh... the Time Displacement Equipment?"
KYLE REESE: "That's right. The Terminator had already gone through. Connor sent me to intercept, then they blew the whole place."
The Terminator (1984)
In fact, according to the official novelisation of the second film, the T-800 from the first film and the T-1000 from the second film were both sent through the TDE before Kyle. Hours later, the Resistance used the TDE to send Kyle through and subsequently obtained a T-800 from cold storage in the same underground complex, reprogrammed it, and sent that through as well. So both assassins and both protectors from the first two films were sent through the same TDE on the same day in 2029.
Lightning burst up from the generator and streaked across the room above the heads of the techs. Winn ducked, smelling the strong odor of ozone. A huge charge of energy was building up. Everyone fell back behind the makeshift barriers and hastily put on their safety goggles. This was going to be big. And Kyle Reese was right in the middle of it.
The chamber below had become a hell of energy with the young soldier at its center. The drone and crackle of the generator built to a pounding thunder. John's heart was racing as fast as the rings. There was a ripping scream, as if a god were being disemboweled. The room filled with hot-white light. Without the goggles, they would have been blinded.
When the glare faded, the floating rings were empty. They slowed to a stop, seared and smoking. In that endless instant of time displacement, Kyle Reese had vanished. Oddly, in its place was a sphere filled with whirling debris: crushed beer cans, faded yellow newspapers, dated 1984, and a slice of a dumpster, filled with garbage from that year.
[...]
John turned from the smoking chamber, seeming years older as his features drained, sagging. He put a hand on Fuentes shoulder for support.
Fuentes realized this was the first time he had seen his commander lose strength. He'd seen him tired, lonely, and haunted before, but not like this. He shouted an order in Spanish to the sapper team behind him. "Set your charges. Let's blow this place back to hell."
John struggled to recover, shaking his head. "Not yet. There's one more thing we have to do." He turned to Winn. "What's your reading?"
Winn glanced down at a palm-sized power meter dangling off his belt. Looked up at John with a puzzled expression. "Just like you said."
John took a deep breath, feeling the wheels of destiny grinding near. Then, mustering his courage, he abruptly strode out of the room. Winn started to follow. Fuentes frowned in confusion and hurried after, grabbing the tech's arm. "What reading? What are you talking about?"
Winn indicated the meter. "This is the energy signal put out by the time displacement. I recorded two other identical pulses as we were fighting our way in here."
"Two?"
Winn impatiently continued walking. Fuentes stayed with him. "What are you talking about?"
"The first one must have been the Terminator going through to 1984."
Fuentes was still confused. "Yeah?"
Winn careened into the corridor and quickened his pace to catch up to his commander. Fuentes dogged the tech. "What was the second?"
"Another terminator, probably."
[...]
The last fragment of uncertainty in John's mind was blasted away. It was time to make the last move in the chess game he had been unwillingly playing with Skynet for fifteen long years. He knew a lot of what would happen, but past a certain point in his memory, he wasn't sure of the outcome. A knife embedded in a weathered picnic table with the words NO FATE carved in them was the dividing line between what he knew had happened and what might happen. His very existence could be erased. Or maybe everything would still turn out the same. Or ... what? For the first time since he was a boy, John no longer had the answers. With growing apprehension, he handed the rifle to Winn, took the probe, and abruptly walked across the room to a heavy steel door covered with a thin sheet of melting ice. John punched out the code and waited....
Ice shattered like glass as the door broke its seal and opened inward. He started to enter when Fuentes stepped in his way, rifle at the ready, and moved inside ahead of him, scanning the room for potential attack. His breath formed in front of him. They were in a coldstorage room. Fuentes gasped as his beam fell on a row of naked bodies, hanging on steel racks suspended from the ceiling.
John panned his light around. There were hundreds of men and women, in rows of ten. Within each row, the bodies were absolutely identical.
"Terminators," Fuentes whispered, his hand on his rifle butt, uneasy.
John quickly walked along the synthetic bodies to the end of a row and hesitated. He scanned the faces. No, not here. Then he gazed down the other row. All the same. Strange to him. Then ... he turned to another row and stopped. It was filled with identical, familiar faces. The broad, brutally handsome features sent a shock of recognition through John.
It was he.
Terminator 2: Judgment Day novelisation by Randall Frakes
As for why Kyle wasn't attacked while he was being sent through the TDE, the novelisation explains that Skynet itself had already been destroyed by that point, and that all the terminators under its direct control were deactivated as a result of that.
Something was happening over on Pico and Robertson. John raised the glasses again and zoomed in on an aerial HK, suddenly spinning out of control like a Frisbee, slicing down to burst into a massive fireball that lit up the ravaged terrain all around. Somebody had just made a good kill. If they survived, John would decorate them. But two other HKs suddenly tilted at a crazy angle and dropped to the earth, without being hit. In the bright flare of the flaming debris, John saw a bizarre sight; a squad of endoskeletons, standing nearby, oddly frozen in place like toy soldiers, their metal surfaces burnished by the blaze. The flashing of beam weapons lessened, then, miraculously, ceased altogether.
John's forces were cautiously emerging from their emplacements and approaching the frozen machines. Another aerial HK, about a mile beyond the battle, hurled down to a fiery death. John was astonished to see the sky suddenly clear of gunships. He scanned the battlefield. None of Skynet's machines were moving!
And then an awesome thing happened.
It grew quiet.
Now all John could hear was the high wail of the wind. No guns. No explosions. No turbine whine or grumbling engines. Even the radios behind him fell silent, until one voice spoke out, the awed emotion detectable under howling static: "This is New Orleans Division. They're not moving! They ... just stopped!" Another voice came on the line, more excited: "This is Chicago. HKs are falling ... my God, they all crashed — " Another voice overlapped: " — San Francisco reporting. I don't get it. The terminators are just standing there—" Another: " — nothing came out to stop us. We're inside the factory now and — " Then all the radios from all the battlefields began to babble the news. But John already knew what they would say. Had known it for most of his life.
Lieutenant Fuentes approached and stood alongside John, gaping at the scene beyond. He spoke so softly John almost couldn't hear. "Just got confirmation....Skynet has been penetrated and destroyed."
The two men looked at each other, their faces blank with shock and the awareness of how inane the monumental can seem. "The war is over, John. We won."
Terminator 2: Judgment Day novelisation by Randall Frakes
There were still some terminators operating autonomously, but the Resistance fought their way through them while approaching the underground complex containing the TDE, and spent three hours clearing that complex before they sent Kyle through.
They didn't just walk in. Although the mainframe computer in Colorado had been destroyed, there were hundreds of autonomous terminators not under direct link command, still free to seek out human targets, and eliminate them. Their internal power cells would keep them lethal for over a hundred years. John realized that the casualties would continue to mount, even after the war was won, until all the terminators could be eliminated.
They had to fight their way past a dozen wild card terminators into the complex. Three hours later, the place had been cleared out. John's handpicked sapper squad formed a protective phalanx for John and the tech team as they rode a huge freight elevator deep into the bowels of the building. They were tiny figures on the open platform that descended at a forty-five-degree angle into the concrete-lined tunnel, rapidly becoming a speck in the overscaled industrial landscape.
Terminator 2: Judgment Day novelisation by Randall Frakes
Terminator Genisys is probably the weakest film in the franchise, but I like the opening scene, which shows the Resistance capturing the complex containing the TDE and Kyle being sent through to 1984. This isn't the original timeline from the first film, so the version of events shown here should be taken with a pinch of salt, but for the most part, it's pretty close to what was described in the first film and the official novelisation of the second film.
Terminator Genisys (2015)