There was really no basic need for currency exchange when the coins themselves were made of precious metals. Conversions could easily be based on the quality and size of the coin itself.

A polity might mint their own coins, but this did not inhibit the use of others.

If an empire was successfully repelled by one of its colonies, would the colony keep using the empire's currency?

This question is unanswerable, as it is based in a fundamental misunderstanding of medieval politics. Empires did not create "colonies". The closest we get is that some have argued that the Crusader States were a proto-colonial venture, but those people are wrong. Thus, the question has no basis in historical reality.