Property insurance damage need advice

[Logan Larochelle]

So I have a Pine  tree that fell and broke my fence, but the main problem is that it has not completely fallen and the fence is holding the tree up at the moment and it is leaning over my neighbors house.

So my problem is I called my insurance company they said they will send a adjuster to asses the damage but they stated  I need to call a tree company and have the tree removed and that I have to pay for the tree to be removed and they will re imbursed me. So I have to pay $1,500 to the tree company and $1,000 to repair the fence first? Shouldn't the insurance company pay for this? (Or how does it work) 

When it's all said and done I pay $2,500 out of pocket for the work then I pay a $1,000 deductible  to my insurance that's $3,500 out of pocket to only have to wait for a check by my insurance company, this doesn't sound right to me