Sustain tail carries over when recording

I'm recording piano in sections, punching new sections as I go (I'm in Reaper).
So I record the first couple measures. When I record a subsequent part using "time selection auto punch" the newly recorded part will often "grab on" to what the sustain was from the end of the first recorded portion (and it won't "unsustain", so the 2nd section all sounds like a big "mush" at least during recording).  I've gotten around it by creating a totally new track using a new copy of the same instrument, and then moving/tacking on, that newly recorded part into the first track. But that strikes me as an odd way of doing it. This may be a Reaper DAW problem, but I thought I would check here to see if there's a setting in Pianoteq that could be causing the sustain to latch onto the previously recorded sustain.
thanks