If a unit is being targeted by alpha strike and would die, but then you reveal a temporal breach saving the unit that would have died to alpha strike, do you get to re-choose who alpha strike is targeting?

No — you don't get to re-choose Alpha Strike's targets.

Temporal Breach banishes the unit, and Banishment is a non-board zone (Rule 56.1). Per the Flash/Repulse ruling, when a target moves to a non-board zone the targeting relationship is severed — Alpha Strike stops targeting that unit, and when Temporal Breach replays it, it's a brand-new game object (Rule 124) that Alpha Strike never chose. It won't take the damage.

At resolution, Alpha Strike just deals its Might in damage split among the remaining original targets. You re-decide the damage split at that moment (Rule 355.14.e), but you can't pick new units that weren't chosen at finalization (Rule 355.15). If the saved unit was the only target, the damage instruction does nothing — no new targets are selected.