Your FAQ says the new app auto updates.

A 'check for updates' button is preferable for me....allows the USER to decide when/if an update occurs. I would rather linger slightly behind the latest version (watching for fallout), than to have a system that drops dead after automatically installing a poison pill. It's also a karma win for you: If I ever hose my install, it's moreso MY fault for choosing to update, rather than squarely YOURS for pushing the update upon me.
Actually, you always have the ability to decline an "auto" update. I should be more clarifying in the FAQ. It will auto check for updates, and still give you the option to decline before performing the update.
Forgive my ignorance on how Android updates propagate.

Is the update downloaded before prompting the user for permission to install? IF the day ever comes that I want to SKIP a revision, I'd want to know that I was accepting a specific update, rather than the file previously rejected.
The way the update works is, I check the sever to see if a new timestamp occurred on the APK. If it does, I prompt the user to ask them if they would like to upgrade. If they choose no, it won't download the APK at all. If yes, it overwrites their previous download on the phone and installs the update.

Feel free to save previous APKs if you would like to keep a history to go back to if needed.