firefox - How can this website reidentify me even after deleting all of my brows...

How can this website reidentify me even after deleting all of my browser's history and using a VPN?

The website dropmail.me is able to successfully reidentify me (and offer my last used temp mail addresses via. "Restore access") despite doing the following:

• Delete all my browsers history which includes cache, cookies, website settings, download history, search history, browser history and active logins. Basically everything that can be deleted through the Firefox menu. I'm using Firefox 52 ESR.
• Use a VPN (that according to their claims is safe against IPv6 and DNS leaking) that I have not used when I previously visited this website.
• Using uBlock Origin and uMatrix

Additional information:

• My "identity" must somehow be bound to my current browser profile. When I use a different browser or a new browser profile, the website doesn't reidentify me as the same person. Actually, it is sufficient to use the Firefox addon Priv8 and create a new sandbox to be identified as a different person. This might indicate that there is some kind of storage for websites that can't be accessed or deleted though Firefox. (It's not Flash cookies, the website doesn't use Flash!)
• (Update) Other browsers are not affected. Microsoft Edge, after deleting browser history, doesn't allow reidentification. This is a Firefox-only issue!

My questions are:

• How on earth are they able to reidentify me? Since their only motivation to reidentify me is to offer access to previously used mail addresses, I don't think they use any "dark" techniques like fingerprinting, but of course it can't be ruled out.
• How can I protect from this kind of "super-tracking" used by this website?