The exchange rate would not get "set up", it would develop naturally based on supply and demand. Just like it happens with currencies on Earth.
First, let's consider a scenario which does not require any currency exchange. Let's imagine you are a trader on TechWorld and you want to make a profit by trading with MagiWorld. You know that there are some TechGoods which are abundant on TechWorld but very sought out after on MagiWorld. Similarly there are MagiGoods which are easy to get on MagiWorld, but very popular on TechWorld. What do you do?
- You use your TechMoney to buy TechGoods
- You travel to MagiWorld
- You sell your TechGoods for MagiMoney
- You immediately spend that MagiMoney on MagiGoods
- You travel back to TechWorld
- You sell your MagiGoods for TechMoney, and. And if you were a clever businessmantrader, you endedend up with more TechMoney than you started out with.
In that case you don't need an exchange rate, because you only trade in local currency for local prices.
OK, but what if you only want to import something but don't want to export anything? You can't easily obtain MagiMoney, because you don't have anything to sell on MagiWorld. So what you need to do is find someone on TechWorld who has the opposite problem: They are exporting but not importing anything, so they have a ton of MagiMoney which nobody on TechWorld accepts. So you go to them and make a deal with them to buy their MagiMoney for your TechMoney, so you can travel to MagiWorld and go shopping.
The exchange rate between MagiMoney and TechMoney would be driven by supply and demand, which in turn is driven by the foreign trade balance. When a world exports more than it imports, then there will be a surplus of foreign currency in that world, so its price will go down. But when a country imports more than it exports, then foreign currency on the market will become less and the price for foreign currency will go up.
Note that with just two worlds, this is a self-balancing system. Cheaper foreign currency encourages imports and more expensive foreign currency encourages exports. So the balance of trade is going to reach an equilibrium.