Do you have a contractor agreement (or similar) with the contractor that sets out who is responsible for expenses incurred at work, etc.?
If not, it may be a case of coming to an informal agreement with the contractor (e.g. contractor pays or 50/50). Safe travels!
Agree with John R,
If the insurance policy is in your name, and there's no agreement with the contractor about the contractor being liable for insurance/insurance excess, then my understanding is that you're still on the hook for paying your insurance excess when you make an insurance claim.