I think there's no way to detect Reincarnation since it's a passive and not a castable ability. You can try though to check if reincarnation is detected by triggers, in that case it would be easy, but I doubt so.
If it's not possible to detect reincarnation or a unit is revived event or something, you can just start a local timer and set hero hp = 25% when the timer reaches 0, which would have the same duration than the reincarnation time to revive.
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Another way is
Trigger 1: "A unit dies -> Unit has reincarnation -> Add unit to DeadGroup" / "Start Trigger 2
Trigger 2: Every 0.5 seconds -> Pick every unit in DeadGroup and (If Unit is alive) set Hp Percentage of unit to (Integer to Real conversion(Reincarnation lvl x 25.00)) / Remove unit from group. / Stop trigger if group is empty
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Doing what Death-Blade says is leakless, MUI and "Unbugable"... Unless you make it bug somehow