For the record, I've spent the last few months trying to debug ArcGIS addin versions and the situation seems to be this:
When you manually install an addin (by double clicking on it), it is copied to %My Documents%\ArcGIS\Addins\Desktop%BUILD NUMBER%, where %BUILD NUMBER% is the ArcGIS version you used to compile the addin. Addins are forward-compatible, so you need to compile on the oldest version you support (for us, this is still 10.0. I know, you tell our clients to upgrade!). When you build your Visual Studio project, this file is updated.
Every time you start ArcMap (or ArcCatalog if your addin works there too), this addin is unzipped to the C:\Users\%USERNAME%\AppData\Local\ESRI\Desktop10.3\AssemblyCache folder and should overwrite the files there with the new version. Sometimes Windows can't do this for various reasons (permissions, file is open elsewhere, etc.) and the addin doesn't update.
The situation is complicated when you attempt a network install of your addin. You can set a registry key (HKEY_LOCAL_MACHINE\SOFTWARE\Wow6432Node\ESRI\Desktop10.3\Settings\AddInFolders), which tells ArcGIS of a network location for an addin. If this key is available and the network location contains a .esriaddin file, this file is unzipped to the AssemblyCache folder instead of the file in Documents\ArcGIS\Addins.
Because the addin is unzipped into the AssemblyCache folder every single time you start ArcMap, you are never quite sure if the right version of your addin is installed. We ended up adding lots of code to check these locations and compared the addins there to the installed version, then warned the user if there was a mismatch. Apparently it's all fixed at 10.4 though. We'll see...