Nothing happens, the page just reloads (like if you were pressing F5) and you're still a guest (in case you were trying to login) or you're still logged in (in case you were trying to logout). It's a random behavior and only happens with Chrome in Incognito Mode on Android... on my Windows 7 PC it never happens.
I can't reproduce anything like this. Make sure you test on the same wifi connection as your desktop to take out any variables.
But really, login issues (user specific) can really only be down to browsers not getting cookies, IPs changing, or the login form not being submitted correctly. Logout issues would be down to cookie removals not being sent/ignored or the logout form not being submitted correctly.
This is something I'd have to be able to reproduce to debug, or at least have a network trace from the before and after pages (including the post requests submitted) to make any sort of guesses.