Yes. Just like any other iOS application, it is linked to your Apple ID. Your Apple ID can be bound to up to 10 iOS devices, according to Apple. Your iPhone, your iPad, your child’s iPod Touch might all have apps bound to your Apple ID and thus be able to run any app you have purchased.
Purchase of the base application is shared via Family Sharing.
Family Sharing does not support the sharing of in-app purchases such as any subscriptions as they are tied to one Apple ID. However, Roomie Remote will share your subscription as part of your owned Home with anyone to whom that Home is shared for as long as they are activated to that Home on their device signed into their Apple ID.
Roomie Remote shares your in-app purchase associated to each owned Home as configured on the owning Apple ID. Purchase the in-app purchase subscription inside the V6 app in Settings > About. The subscription must be made from at least the V5+ app – this method does not apply to subscriptions from older apps before Apple introduced the new subscription system in 2017. That type of subscription will be associated with Owned homes you create. The in-app purchase is associated as part of your Home and all other devices including those you have shared to will observe that subscription when activated to that Home. Note that the 8 and 24 subscription levels are limited to a single owned home.