Because of the glitch, we weren't sure if my side even signed it or not; but essentially, yes.
What happens is, I create the TX from my side, and it automatically appears on their Guarda client for them to sign.
In this case, I'd create the transaction, but nothing would appear for my partner.

Recovery was more confusing as inputting private keys alone on Electrum for example would not show our multi-sig wallet.
Also, we were not able to individually sign transactions putting our private keys onto electrum; we could only broadcast but not sign.
So we had to find another solution that worked - which is the above.