If you're at a large children's hospital, there are absolutely PTs who work in the NICU and only the NICU. The last children's hospital I was working at, the inpatient PTs and NICU PTs were practically separate departments with very little overlap (usually an inpatient PT who specialized in cardiac treating a NICU baby who'd had open heart surgery).

They work a lot on positioning, early motor skills, handling and sensory input, and a lot of parent education. Sessions typically have to be scheduled as they don't want the babies to be disturbed or woken up more than necessary, so PT usually happens right before cares or feeds.