What is the agreement with the person doing the drum session? What are you paying for?
Comparing apples and oranges, but, as a writer, if I write something, if I write a story for someone, it’s still my creation, and I retain copyright. Unless the agreement with the person whom I wrote it for states otherwise. Then they can do what they want with it, per our written or verbal agreement. When I interview someone, I ask them if I can use their words in my book, and I tell them that they won’t be compensated, unless it is a deal.
As a keyboardist, I don’t want someone copying my cool riffs, without some attribution or payment.
Most musicians won’t even let you use the title of their song in a written work without permission.
Drummers just make a lot of noise, not music, AFAIAC, so I don’t understand how anyone can tell the difference between one drum solo and the next, but I’m sure they think very highly of their work!
It’s basically, what is your agreement or understanding with the person you hired? Actually, just what is the agreement, because you two may have differing “understandings.”