Yes, it is supposed to work like that (saves progress in your browser, not account, but same idea). Does it even not work if you manually save in the settings and then refresh a second later?
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OK, thanks for clearing that up because then it's my fault. I have set my browser to never remember browsing history and cookies (that's just an odd personal preference of mine) and if the save data is saved in the cookies then it obviously won't work. Looking forward to the update though because I like the game very much so far.