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I don't know specifically. There are several ways to do this. Flash Player itself could do a check and download a new copy, but this would be pretty hard to do. Normally, you'll have a program that runs every time you log into Windows that checks for you. This itself can be found in one of several places depending on how it was implemented. You might find it in Start > (All) Programs > Startup. More commonly, it's hidden away in the Registry to make it all the more awkward and irritating. You would think that Adobe would let you choose whether to run these checks during installation, but I am assuming not! I don't run their installer any more: I install Flash straight into Firefox using the Firefox plugin finder. I don't recall if I got a choice in the past, but I don't think it ever forced me to upgrade.

Assuming there is no such setting, how do you get rid of this feature?

If you have Windows Me or XP there is a supplied tool to help you track these down, called MSConfig, but the preferred tool for this is called Autoruns:

http://www.microsoft.com/technet/sysinternals/SystemInformation/Autoruns.mspx

If you install this, run it and switch to the Logon tab (bottom row, 2nd left) you can see everything that starts up when you log in. You should see the Adobe Flash update checker program in there: simply untick it and it won't run any more. (Or you can delete it for good by selecting it and pressing delete (not backspace).

I must caution you that Autoruns is a deadly serious program for experts only, abuse of which will make your computer a complete wreck. Don't alter anything you don't recognise :P