In The Force Awakens we see Poe talking to Lor San Tekka and receiving the map fragment, and then the First Order suddenly shows up. Is there anything in canon to indicate whether Poe was followed to Jakku, or did the First Order just happen to independently discover that clues to Luke's whereabouts might be on Jakku and also just happen show up at the same time as Poe?
According to Star Wars: The Force Awakens - Storybook the First Order found out about Poe's mission and went to take the map from him. It is unclear from this if they already knew that the map was there but it seems unlikely.
The First Order had discovered Poe's mission. They had sent a platoon of stormtroopers to capture Poe and take the precious map. Already, they could hear the him of ships landing at the edge of the village.
Star Wars: The Force Awakens - Storybook
This was addressed in the canon novelette, Star Wars: Before the Awakening - Poe. In short, Leia had become aware that a Senator named Erudo Ro-Kiintor was in cahoots with the First Order and had been dealing in information in return for money and influence. She had Poe raid his vessel and seize some info that he'd uncovered about the location of Lor San Tekka, an archaeologist with a deep knowledge of the Jedi Order and who had been working with Luke on uncovering the location of the first Jedi temple.
It's worth noting that they're not after a map (per se). Both Leia and Kylo Ren/Snoke simply think that Lor will know exactly where Luke is.
We obtained a lot of information from the computers aboard Hevurion Grace,” Leia said, looking at the chip. “A wealth of information. But there was something else, something that…others may have missed. A piece of a puzzle I’ve been working for…for a long time to solve.”
She set the data chip in Poe’s palm.
“I think the First Order is trying to solve it, too, Poe. We have to solve it first. We have to find him first.”
“His name is Lor San Tekka.”
“Lor San Tekka,” Poe repeated. “Why’s the First Order so desperate to find him?”
“They think he knows something. I’m hoping he does, too.” Leia took his hand and folded his fingers closed over the data chip. She met his eyes. “I’m hoping Lor San Tekka knows where to find my brother, Poe. And Luke Skywalker may be the only hope we have left.”
From the point that Poe returned to Leia with the info, he only had a few hours head start before the First Order also received the same information and headed off to Jakku to find Lor, hence why they arrived at Jakku almost simultaneously and both headed to the correct village.