Categorisation of earnings regulations

Could somebody please clarify the rules in theses particular scenarios?

I have a client who runs a cleaning business and engages self employed workers. The business cleans both commercial and domestic properties. If my understanding of the regulations is correct, my client should be operating PAYE and applying Class 1 employee and employers NICs on the workers but not deducting tax (ie use tax code NT).

As a note for future reference, if my client only provided cleaning services to private dwellings, would they then be exempt from applying this treatment (as per ESM4018) or does this rule only apply to workers employed directly by the owner of the domestic dwelling i.e. does the fact that the worker is engaged through a 3rd party business mean that NICs must be deducted regardless of the type of property being cleaned?

And in addition, do residential lettings count as domestic dwellings for these purposes, for example where let properties are cleaned in between tenancies, is this cleaning work deemed to still be for domestic dwellings (even though it is investment property)?