for most messages encryption is done by proton when they are received, because most of them are not end to end encrypted. while doing that they can just forward the original no issues. I have no idea though what can they do with messages sent from another proton account, as that's end to end encrypted. maybe they forward the PGP encrypted message?

tutanota won't cause any problems because messages between proton and tuta are not end to end encrypted (unless you manually set up PGP encryption, which you can do when sending to any other email providers).