A dummy unit with locust and a life regen aura can choose targets so you can make allies be healed but not enemies for example.
The trigger does not necessarily need the ability to work.
You can also group all units inside the region and increase their health.
This is a much bigger operation but doesnt require an ability.
For the ability trigger version, you have two triggers.
1, if a unit enters region r and should be regenerated, give ability
2, if a unit leaves region r, remove ability