Fran, I always feel DB pullover in my tri's! One of the reasons I
this exercise so much is that I feel it from my elbows, up my tri's, then all the way down to my waist. Wow - lots of muscles!
Some people call pullovers a back exercise; others (like Exrx.net) call it chest because it targets the serratus, in between your chest and back. That's why you feel your tri's - which you don't in an ordinary back exercise (where you typically use your bi's secondarily). But I'm like you and include it on back day. It's my favorite back 'finisher'.
But I feel a lot steadier when my whole body is supported by the bench, not just my upper back (my feet are up on the bench). I see a lot of people with their necks and spines out of neutral position in the way you're describing - people's heads tend to hang down that way and they arch their backs. Just something to watch for.
Move Question: Dumbbell Pullover while Resting Upper Back only on Bench
Maybe it's because you're using a heavier weight than I am (the most I've ever done is 50#) and/or your tri's are a heck of a lot stronger, so perhaps you don't feel it the way my poor weak triceps do? 
