Pretty sure you get to set aside another card, but Island stays in the trash.
Imagine if instead of playing Feast, you played this hypothetical card:
HypoCard - Action
+2 Cards
Place this card on top of your deck. If you do, shuffle your deck.
As far as I know, this could be a legal card. Now, the LoseTrack rule would apply to it just as it would apply to Feast or Madman; if you play Procession on HypoCard you get +4 cards, but it stays in your deck rather than being trashed.
Now, imagine if you had Throned a BoM, first choosing HypoCard and then choosing Island. Surely it would be wrong for the HypoCard to be pulled out of your deck and set aside on your mat, just as it would be wrong for Island to be pulled out of the trash after a Feast.
(edit: Probably don't even need a hypothetical card for things to get confusing. King BoM, choose Feast, then Graverobber to gain your BoM from trash, then Watchtower to topdeck, then Island, etc)