Toshiro Umezawa
You choose whether to return it to your hand or to exile it. If you recast it, it's not affected by Toshiro anymore.
Normally, when an effect both moves a card and does something based on the card, it looks at the object the card was in the previous zone. Here it doesn't make sense, so it affects it in the first public zone it goes to. Thus, “if that card would be put into a graveyard this turn, exile it instead” applies to the card on the stack. If later that card changes zones, it's a new object and is not affected by this. No effect can track a card through multiple zones.
Now, second point, when you cast a card with buyback thanks to Toshiro, it's affected by two replacement effects when it finishes resolving and tries to go to the graveyard. As the controller of the card on the stack, you choose which replacement effect to apply first. If you choose buyback's replacement effect, Toshiro's does not apply anymore (the card is no longer about to go to the graveyard). Similarly, you can choose to apply Toshiro's replacement effect first, and buyback's will not apply anymore.
Note that neither of those are self-replacement effects, since for Toshiro it does not replace its own effect, and for buyback it does not replace the effect of the spell but a game rule (that you put a spell into it's owner's graveyard as it finishes resolving).
Daniel Kitachewsky
L3, Paris, France
Rules NetRep