By default there is no communication with relays and no public info displayed about your tips. Like Ava said, it's no different from seeing an XMR address on someones nostr profile and sending them Monero, but just slightly more convenient.

The other two options DO compromise anonymity/privacy because you're making it public. There is going to be a new bounty to make those options more anonymous/private though and hide more info from relays. For now I would stay with the defaults to be safe.