I have found that this issue can be caused by a configuration setting in the add-in file.
Check the config.xml for the add-in for the following section:
<Targets>
<Target name="Desktop" version="10.2" />
</Targets>
As long as your add-in code is compatible with 10.1 functionality, then changing this setting to 10.1 should make the add-in available to the user.