I'm not whether "a person occupying the same premises" is causing or suffering the nuisance so I will address both.
A tenant is the controller of the premises. As such, whatever they or any of their guests do is legally the tenant's responsibility. If a house-guest or child of the tenant is playing the trombone at 3am and causing a nuisance then it is as though the tenant were doing it themselves.
Similarly, the household of the tenant cannot, at law, cause nuisance to itself. If guests of the tenant are being annoyed by the tenant or vice-versa then they may have a legal case: just not under real-estate law.
In this phrase "nearby" means property outside the tenant's control but close enough to be affected by the particular nuisance. For example, a property with no line-of-sight to the tenant's property cannot be nearby for a visual nuisance but can be for a sufficiently load audible one.