One site logs the other out in the same browser

I have two 2.2.1 Cake sites open in the same browser (doesn't matter if it's Safari or Firefox). If I log in on one, then go to the other and log in there, when I go back to the first site I find I am logged out (and vice versa). I can log into both if each is open in a different browser.

- Both have their own full cake directory (they are not sharing a core)

- Both are using database sessions (I have tried flicking one to use cake sessions, but the problem persists)

- Both have different Security salt and cipherSeed values

- Both have caching disabled

Where do I look for the cause?

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