Priority, simply put, is the right for the turn player to act first.
My opponent can still "respond" to my summon (if possible: See "
Exiled Force") but
I have the right to go first as the turn player. Having "
Pineapple Blast" set on the field doesn't give me the right to activate it before my opponent can do anything. All it dictates is WHEN it can be activated. Same with "
Torrential Tribute", "
Bottomless Trap Hole", "
Trap Hole", etc. I still retain priority after the summon to do something first. So if I want to go ahead and TT the field, that is my choice. Feel free to chain BTH to it and make my guy be removed from play instead. If I wanted to I could "
Trap Hole" my monster (say I had "
Last Will" previously activated), see my opponent chain "
Book of Moon" to prevent that from happening, only to then chain "
Pineapple Blast". The timing is still correct. I normal summoned a monster (the last event to occur since the chain hasn't resolved). But look, it's 3rd on the chain. Or say "
Stumbling" is on the field... I lose priority then so now my opponent can chain to the triggered response. I could still drop "
Pineapple Blast" at this time. But, I only lost priority in a triggered sequence. Otherwise I am more than free to decided what I want to do first, if anything.