Ah! That's what happened:
In the "Add cosigner" dialog of wallet creation, I was presented three options:
- Enter cosigner key
- Enter cosigner seed
- Cosign with hardware device
Because the cosigner wallet was on my Android smartphone, I preferred the seed rather than the public key because the seed would be more convenient to type by hand. I didn't want to transfer anything electronically (which of course, thinking about it, is not dangerous at all with the public key).
Naively, I thought that from the seed the cosigner's public key and ONLY the public key would be derived. I wasn't aware that also the cosigners private key would be stored and thus cosigning would then be done in the same wallet that initiates the transaction. In other words, more or less unconsciously I assumed it wouldn't be implemented that way because that would make multisig pointless (that was my idea at least).
Wow... it's really not for newbies
... and I still didn't leave the newbie state entirely behind me... at least I'm already smart enough to search for a better bitcoin storage than an exchange
As a follow-up question, what's the use case then for the "Enter cosigner seed" option?