It can happen at both sides but very frequently happens on the receiving end.
If you transfer, for example, 100 EUR from an IE IBAN (EUR) to another IE IBAN (GBP), the sender bank will not always know that the money is going to a GBP account, they will just see the IBAN code. The receiver, will do the FX to GBP provided they allow EUR to be deposited in a GBP account, which they normally will because they can profit off the FX margin that is at their discretion.