HELP! Tenant Property Damaged from Sink Drain -- my liability?

My painter was washing his brushes on the second floor using a sink that's not been used for over 10 years.  The 1st floor commercial tenant alerted me that water from the ceiling leaked all over their computer/printer/desk/chairs.  The 2 units have separate lease.

My property insurance said the tenants' personal property is not of my interest so it's not covered under my property insurance.

Should my liability insurance cover this?  Or would their rental insurance cover this?  

I offered to help clean up since the damages seem mostly superficial to me.  The tenant wants to go through an adjuster from my insurance.

Would like to resolve this the correct and responsible way.

Please help thanks!!!