I'll go ahead and answer that it can't. It knows I'm mullvad user X, thus deanonimization, "it knows I use mullvad", but it doesn't know my original IP, so "it doesn't know I'm me".
But when you connect to the site from via server A and later via server B they can tell that you're the same person.
And they can deanonymise you through data brokers. All Mullvad IPs are traceable back to the same number (acting as a pseudo account identifier) so if you ever entered your PII on any website when using Mullvad, it can be linked to the same Mullvad account.
And if you ever visited any of those sites without using a VPN, your home IP can be linked to your Mullvad ID through browser fingerprinting.
And if you ever entered any PII on any website from your home IP, you can once again be deanonymised.
Now the existence of browser fingerprinting isn't Mullvad's fault, but this flaw makes it a lot easier to accidentally deanonymize yourself.