who pays the costs of a dehumidifier?

My tenants are causing condensation damage to my property despite being adamant that they are not (I'm not blind/ or stupid) I've had a specialist out who confirmed that there appears to be no underlying cause and that they are not making full use of the windows/ heating/ air vents.

I have passed on advice from the specialist on 'how to live in the property' but if they do not adhere to this how do I prove they have neglected the propety and caused the damage, and therefore will it be at my expense that I will have to redecorate?

If I offer to buy them a dehumidifier who will be liable for the electricity bills? or should I not do this at all?

I've noticed a few condensation/ damp posts- obviously the time of year!!!