Card text says: "When this card is Synchro Summoned: This turn, this card cannot be destroyed by battle or by card effects, also you take no damage."

I synchro-summoned it fine. Used it to attack the enemy on the same turn. Enemy was somehow able to use Dimensional Prison on it and it counted as a legal card move.

Again, AI battle, so no replay.
Dimensional Prison does not Destroy anything. It just Banishes an attacking monster meaning Powered Inzektron is not protected against it.