Should my photographer build the tour in my account or in theirs?

Have your photographer build the tour in your account, unless they would rather keep it in theirs until you are happy with it. In your account the tour is yours from the start: you make it with a first photo, invite them as an Admin (if they design it too) or an Editor, and only you publish it and choose its hosting. If you are on Free, your photographer must be on Pro, Agency or Enterprise; from a paid plan any plan works for them. What they upload counts against your account (250 panoramas on Free).

If they build it in theirs, they hand it over. That is part of the Pro, Agency and Enterprise plans. You look at the tour first, then take it over with a Vault, which you pay for unless they offer one of theirs that goes with it. They can stay on it with the access they choose.

A third way is for them to send you the photos to upload yourself. Let your photographer build the tour in your account and Take over a tour from the person who made it have the steps.