My pool contractor has done some damage to my neighbors property and he is very angry am I’m liable if the pool company doesn’t fix it to his expectat

I am sorry to learn of this unfortunate situation.  While you may be ultimately liabile if your neighbor were to sue you, hopefully the pool contractor you engaged is properly licensed and insured.  Typically contractors carry General Commercial Liability insurance which is designed to cover personal injuries or property damage resulting from their activities.  As a practical matter, if pool contractor does not make things right, getting neighbor pool contractor's insurance information and to allow neighbor to make an insurance claim would be the first step in this process rather than neighbor suing you.  I wish you luck with this situation.