Short answer: Yes. Every membership tier belongs to exactly one project. A tier does not grant access across your catalog.
Choose what a tier opens
Open that project's Monetization page, choose Memberships, and create or edit a tier. Choose Everything in this project or select the scenes it unlocks.
When creating a higher tier, it must include the scene unlocks already granted by lower tiers on that project. Tiers on a different project have an independent access ladder.
If you offer memberships on several projects, create tiers on each project. Naming a project in a tier's description does not replace its access settings.