That your tenant owns other property is neither here or there, but................
The other house is their normal place of residence.
At least one of the joint tenant in the tenancy needs to "occupies the dwelling-house as his only or principal home". If not, then tenancy is not assured. It being a common law tenancy is not necessarily an issue from the landlord point of view since the difference is the tenant losing a lot of the protection offered by assured (shorthold). However, the fact that you won't necessarily know at any given time whether the tenancy has become or cease to become assured may be.