The vehicle owner is ultimately responsible for payment for all repairs.
You may instruct your insurance company to make payment directly to the repair center on your behalf. Usually, an initial payment is made for the repair estimate and then during the repair process, a supplemental payment will be issued for additional hidden damages or parts cost that is discovered during repairs.
The collision repair center can assist you with clarification on any payments that may be issued. This can also get you back into your own vehicle in a timelier manner.
Remember to clarify any deductible amounts or questions you may have as early as possible. Your portion (if applicable) is not required until the completion of repairs and you pick up your vehicle.