Employment law has the distinction of "employee" or "independent contractor".
If you hired a handyman without any license, usually this person is your employee, even though he only worked for you for as little as one hour. As his employer, you are liable for everything he does.
If you hired a company/individual with a license, usually this person is an independent contractor. You probably won't be liable for things went wrong other than your project expense. Note you have to hire contractor with the right license, if your electrician is doing your plumbing, the electrician is not independent contractor for the plumbing work, he is acting like your employee/handyman for the plumbing and you are on hook if things go wrong.
These are general rules, I don't know your project and your contractor, so look into state law.
For example, your rental unit need electrical work. You hired a handyman to fix it, and later somthing went wrong and the tenant got electrocuted, well, handyman has no license and you as employer will be liable for tenant's injury.
Now, had you hired a licensed electrician, and later tenant got elecrocuted, tenant could go after the electrician's insurance to get compensation.
Capish?