I traveled to Nepal with TPS AP for two weeks and came back a week ago. Did not encounter any problems with immigration coming back. My entry point was JFK. After getting my passport checked and finger prints taken at the Visitor Queue, was then directed to a separate room. Had to wait about 15 minutes, the parole officer verified my AP document, stamped it and told me to have a nice day.
That was my experience, in my opinion as long as you do not have a criminal record and all the info on your passport and AP match up perfectly you won't have an issue coming back. There was a lady stuck because her name was spelt wrong way (lastname firstname) on her VISA. I believe she was detained overnight.