Once an Assassin creature or commander you control deals combat damage to a player in a turn, you can cast spells for their freerunning costs for the rest of that turn. It doesn’t matter what happens to that Assassin or commander after that.

You pay all costs and follow all normal timing rules for cards played this way. For example, if one of the exiled cards is a land card, you may play it only during your main phase while the stack is empty.