Error in "Project Manager Approval" Process, is sending timesheet notification to people not involved in the project, when you execute 'Resubmit Action Item' step.
Other users could have 'Timesheets - Edit All' permission, with this permission he will be able to recevie notification from that step.
Also it could be because the resource who receive the notification and does not belong the project is on a group which have 'Resource - Enter Time' permission and that permission is set to enter time for all resources.
Remove 'Timesheets - Edit All' permission
Or/and if required remove 'Resource - Enter Time' permission from the group