According to the documentation the add-in should work with Office 2010:
The Teams Meeting add-in is automatically installed for users who have Microsoft Teams and either Office 2010, Office 2013 or Office 2016 installed on their Windows PC. Users will see the Teams Meeting add-in on the Outlook Calendar ribbon.
I'm currently testing with my customer without success :(
Only thing I would think to check is office versions. Make sure it’s in latest SP etc. then log out of teams with outlook closed Making sure the outlook.exe is not running. Sign back in. Then load outlook.