As the Evil Twin is being put onto the battlefield, you choose something to copy. This happens in the middle of the Invocation resolving since it is a replacement effect. Which means it will be a copy of something when the spell gets to the point of determining how much damage to deal. Also note that the damage is being done as the result of a trigger; not the spell itself which means Evil Twin must be a copy of something by that point.
If you put ET on the battlefield with the Invocation, then when it comes to dealing damage, the Twin is a copy already, since its ability replaces the event of it entering the battlefield with it entering as a copy of something else (if you so choose). This happens during the resolution of the Invocation before the spell's other effects happen.
Edit: The invocation has a trigger, which goes on the stack seperately after the spell has resolved. It is that trigger, that causes the creature to deal damage, so you could even further modify the Twin's power in response.
Questions such as this belong in the rules forum, by the way. The thread will be moved there shortly by a moderator. But in the future, please ask such qiuestions there.