The answer is no, you cannot use Master Hyperion's effect on your opponent's turn.
Here's why:
* Effect Trigger: Master Hyperion's effect is triggered when it's Normal Summoned or Special Summoned. This means the effect is only activated when you summon it to the field.
* Timing: The effect specifies that you can "Special Summon 1 "Hyperion" monster from your hand". This action is only possible during your turn.
In summary: Master Hyperion's effect is activated only when you summon it, and you can only summon it during your turn. Therefore, you cannot use its effect on your opponent's turn.