If he was a POI before he left from Pullman to Pennsylvania, FBI must have followed him.
If he became POI after he departed from Pullman, then they must have checked if the car arrived to its address of registration, I.e. his parents home and watch him.
This is what was reported:
'Sources say that authorities knew who they were looking for and had tracked Kohberger to his parent's home on the 100 block of Lamsden Drive in Chestnuthill Township, Monroe County.
Law enforcement sources told ABC News police in Idaho identified Kohberger as a suspect, at least in part, by using DNA technology. They tracked him to Pennsylvania through his vehicle.
The FBI had been watching the house for several days before a specialized team of state troopers and federal agents moved in and took him into custody around 2 a.m., sources say.
Authorities are still working to investigate how Kohberger was connected to the victims.'
One way or another, it is irrelevant whether he was followed all 2500 miles or was followed only during some part of his trip, or was not followed at all.
What is relevant is that he left DNA at the crime scene to enable charging him and that he is not free to kill again.
Pay attention to the last sentence of the quote, they still have to work out how he was connected to victims. That may means that noone from victims inner circles met BK, jmo. Which leaves social media. Scary
The prosecutor said investigators believe Bryan Kohberger broke into the students' home "with the intent to commit murder."
6abc.com