Originally Posted by Mwenenzi

The fool proof way is not to have a frequent flyer number in the reservation. And then retro claim after the flights. But then you could miss any benefits you have from status.
Q "Call the airline, or ask the agent at the physical check-in desk?"
Both, and keep checking. Then check again. And at check-in desks before each flight. Keep all physical boarding passes.
Changing ffn's does not always stick. Any possible combination of errors that may happen will have been reported on FT as some time. Even if the boarding pass prints with the correct new ffn, it could credit to the other. Or any other random combination you can think of.

Manage my booking in AY may help https://www.finnair.com