How can I tell which timesheets I approved and which were approved by my alternate manager?
You can see who approved each timesheet by running the Timesheet Status report with the Detail View option and Approval History checked, for timesheets with COMPLETED, LOCKED/EXTRACTED, or APPROVING status.
The approver is in the BY (FOR) column in the Approval History section. If the approval was done by an alternate, the alternate is listed, with the approver (approved for) shown in parentheses.
If Manager Review is turned on, the Manager has to review the approval. That will be reflected in the PENDING APPROVALS column of the report.
This property for timesheets is
unatime.manager.review.required and can be updated at Admin > Properties > Approval Process > Reviews > Require Manager Review > Timesheet.