Every service that stores your email is another place it can leak. The fewer places hold your real address, the smaller the blast radius.
A temporary address hides your inbox, not your identity. IP address, browser fingerprint and anything else you submit can still identify you. It is a spam and exposure tool, not an anonymity tool.
It hides your real address from the service, but it does not hide your IP address or other details you provide.
Anyone who knows or guesses the exact address can open it, so treat every message as public.