I don't think the characters are doing anything especially impressive here.
Sarah manages to get most of the way to the elevators on her own. John and his pet Terminator show up just as the T-1000 does. The most remarkable thing she does at this point is to trust the Terminator, albeit with serious reservations. They watch as the T-1000 melts through the prison bars, which is enough to get Sarah, John, and the T-800 up and moving again.
With the guards and doctors now out of the way, the group has only one enemy to deal with. As such, the obvious move is now to shoot that one enemy as many times as possible. Therefore, they do so. Sarah has presumably decided that she can worry about the T-800 later, because the T-1000 is clearly the bigger threat. Everyone knows that the most important thing is to get the hell out of Dodge. Therefore, they vamoose.
They run to the elevator. Once inside, it is incredibly obvious that their top priority is to make sure that the T-1000 doesn't get in. Hence, more shooting.
In the garage, a cop car pulls up; it goes without saying that the group needs a car, and they can't afford to lose any time, so Sarah puts a bullet through the windshield and yells "Get out!" The cop is startled, so he hesitates; therefore, the T-800 helps him along and tosses him aside.
They get in the car. Everyone realizes that the priority here is to keep John safe at all costs, so they toss him in the back seat and tell him to stay down. The T-1000 chases them, so no one has to be told that speed is of the essence. The T-800 puts rubber to metal and they race away.
Holy crap, that metal guy is fast! The car is moving as quickly as it can, and with no other options available, the solution is clearly more bullets. Since John's most important job is to not get shot in the face, he has to keep his head down while mom and Uncle Bob do the shooting. He isn't useless, however, so it is only natural that Sarah and the T-800 let him do the reloading. He has spent most of his life learning how to fight, so he is more than capable of doing it.
From this point onwards (and really, this has been the case since they got into the car), there are only two things to do: drive and shoot. This is well within everyone's capabilities, and it is so obvious that it doesn't need to be said. This isn't a real battle: in actual warfare, there are tons of variables, enemies all over the place, and usually, a great deal of confusion. The situation our heroes find themselves in is not so complex - there is one bad guy, and the idea couldn't be more simple: shoot him repeatedly until he is far enough away that you can stop worrying about him. And that is precisely what they do.
Note that at no point during this sequence of events was there any room for confusion about what everyone should be doing. It was always totally apparent that the T-800 was the bulldozer, Sarah was his backup, and John was the guy who had to avoid dying. Sarah's previous experience with Terminators was entirely negative, but she knows enough about them to know that she should let the T-800 do the heavy lifting, whether that means letting him absorb gunfire, letting him go toe to toe with the T-1000, or letting him drive.
For the most part, everyone understood their respective roles without the need for discussion. How did they know this? Because it had been ingrained in them all along. John grew up hearing about his destiny - to be the savior of humanity. Sarah was the one who taught him this, and also taught him everything he needed to know in order to become a military leader. So both of them had already been in this mindset for as long as John had been alive. They had been steeped in a combat mentality for over a decade.
And of course, the T-800's rason d'être was to shoot things. He exists solely because he can fight. Everything else is secondary to his combat abilities. If he wasn't a skilled warrior, he wouldn't have been made in the first place.
So, in a nutshell, there is nothing surprising about three warriors being able to fight like a well oiled machine at a moment's notice. Of the three, only Sarah hadn't been training for this her entire life. John and the T-800 had never known a time when they weren't focused on tactics, strategy, weaponry, combat training, and armed conflict.
Frankly, it would be much more surprising if they didn't work so well together from the word go.