Yes per the card rulings you cast the copy as the ability resolves.

Can you kick spells with Isochron Scepter?

Yes, you may. When you cast the copy, it is just like you are casting the actual card (using the alternative cost granted by the Scepter). As such, you can pay any optional additional costs (and must pay any mandatory additional costs).

Can you cast overload with Isochron Scepter?

No you cannot. When you cast a spell, you can only use one alternate cost. Overload is an alternate cost, and casting a spell without paying its mana cost is an alternate cost. So you cannot choose to overload the Rift cast via the Scepter.