I built an extension for Chrome and Firefox and I am going to release it, soon. Do I have to check for the browser version the user is running or do the stores of Chrome/Firefox automatically check which version is needed and set this as a condition for downloading the extension?
Both browsers offer you a way to specify a minimum browser version in the extension's manifest.
For Chrome: minimum_chrome_version manifest key.
For Firefox (note, this will make the manifest incompatible with Chrome): applications.gecko.strict_min_version manifest key.
I'm not aware as to what happens on first install if the latest update requires a higher version, but an older version that fits exists - needs testing whether an older version will be offered or it will be marked as incompatible.
In case of automatic updates, the users will be stuck on last compatible version. Which makes it slightly problematic to inform them of this..