Insurance laws can and sometimes vary from state to state.
I retired from the insurance claims business. Normally, if a tree is blown onto a neighboring piece of property and that tree is a green, healthy, solid tree. the tree owner is not responsible for damages as no one can control nature--- hence--the much mis-understood " act of god " thing. If the tree was rotten or partially rotten and the owner had cause to know or should have known it could be a hazard, then he ( usually his insurance ) will pay for the damage. Simply being the owner of something doesn't automatically make you liable for damages.
If It came a tornado and blew my roof off and it landed across the street and damaged my neighbors car or house, how could I be responsible? I had no control over the tornado-- I had not created any hazardous situation-- I was a victim the same as the neighbor. Simply because it was my roof doesn't mean I or my insurance co. would have to pay. Basically to be liable you have to have created a hazard or knew of a hazard and did nothing to correct it.
Storms are something most of us ( maybe a few---:king ) can't control--- that's one big reason we carry homeowners insurance.
Regarding the 9 x 5 storage bldg., you owe for what he lost. Nothing bigger or more fancy. If the bldg. was old and rusted, dented, etc. you would be entitled to take depreciation, as he lost an old, rusted, dented bldg. Not a !2 x 18 shiny new one. If his bldg. was in real good shape, I wouldn't worry about trying to take depreciation.
Was your tree a good, healthy tree with no defects--if so, you probably don't owe anything. If it was partially rotten or dead, then you probably do owe. But as said, you only owe for what he lost.
I'm not familiar with the ins. laws in your state but in many cases they are pretty much the same when it comes to this sort of thing. :wave