Hi @ughy ,
If you install an app on your store, the app should function on the site regardless of which domain the user is using to access your storefront. An installed app is added to your store and should not be assigned to a specific domain. If you had multiple stores to which your domains were attached, in that case then the app would need to be installed on each store (and paid for on each store).
Do you have multiple stores or are all of your domains attached to the same account? What app(s) were you looking to install?