When adding or removing a member on the project team, the Last Updated Date for the project is not always updated (it is under some circumstances).
The Last Updated Date is only updated when a Team member is added or removed if this changes any assignments, as there will be updates on some project level attributes (like the ETC curve).
During addition, this will only happen if the Effort Task is enabled (Administration > Project Management > Settings > Staffing > Allow Effort Task Creation), as this will automatically create an assignment in the Effort Task.
During removal, this will happen only if the resource is assigned to at least one task (not necessarily the Effort Task).