Wood Rot in basement floor

[Zulu Black]

I am currently renting out my SFH to a family in NYC

that just had their house burned down last year. Their insurance is currently covering the rent and they are in the last month of their lease. I was notified for the first time by the tenant last night of wood rot in my basement and apparently some of the flooring "flip collapse". I went to check out the situation today and found that 2 of the joists indeed looks like they're rotting. I also found where the water is coming from. 

My question is, can I file a claim to their insurance company that is currently paying the rent against their security? Because yes, it does seem like the joist are rotted and it does seem like the water is coming in from the boiler room but for them to tear up my flooring doesn't seem right to me. I'm not sure of my next step. I currently placed a sheet of wood over the area and notified the tenant to not go down to the basement and that I'm looking to fix it up soon. 

My other question when do I have to do the repair by? They're lease ends in 3 weeks and is planning to move out at that time. Could I wait till they move out to fix the flooring or do I have to fix it now. 
 
 

[Nathan Gesner]

I'm confused. You said the "joists" are rotting but isn't your basement floor on a slab of concrete? Joists are in the ceiling. This appears to be a thin sheet of wood used as sub-flooring with tile on top. Is that correct?

It doesn't look like that big of an issue. Fix the leak in the boiler, tear out the bad flooring, dry it out, install new flooring. It's probably going to cost less than the deductible on any insurance claim and I don't think it would qualify for insurance, anyway.

Unless it's a health hazard, I would wait until the renter vacates so you can work unimpeded.