Universities apply for the transfer of patent ownership.

You and your tutor are both inventors, and they should be job inventions. So the patent right belongs to the school. But if your job is not a service invention, you and your tutor can both become patentees. But since you said that the patentee is the school, the transfer right of course belongs to the school. Only the patentee has the right to transfer the patent, but the inventor has no such right. Inventors only have the right to mark their own names on patented products.