Auschwitz - reservation still required if on a tour?

Ask the tour company.

I did not have to make my own reservation when I visited Auschwitz with a tour company. I would expect that would be the same with other tour companies, as that is a part of the service (and charge) that they typically provide, buying visitor tickets in blocks for their participants.

If it is this tour:
https://www.seekrakow.com/history-tours/auschwitz-birkenau-museum-guided-tour-from-krakow/

The tour description says:
Price includes:
Departure from one of our pick-up points
Transfer by air-conditioned vehicle
Entry tickets [emphasis added]
The care of a professional museum guide
Return to your place of departure

Later on the page it says:
"Entry Pass is valid with an identity card. Remember to take documents with your name and surname."

That would seem to indicate that they will arrange the tickets specific to the participating tour members.

This sounds very much like the Auschwitz tour I took. (I booked and paid through my hotel, so I am not certain.) When my tour description said that, all I had to do was show up. But you could always use their email on this page to confirm:
https://www.seekrakow.com/contact/

Quick tip: bring some small change for the restrooms in the welcome center. In 2018, it was 4 złoty (about $1 US.) I don't recall whether it would have been possible to pay at the desk using credit card.