How can I ensure that my Hiring Managers are reviewing the details of each Invoice before approving?

In Settings —> Approvals, you can turn on a setting to turn on Work Order Matching Confirmation. 

When this toggle is turned on, your approvers will have to check a box on Invoices that do not match Work Orders providing additional confirmation acknowledging that the Invoice does not match the Work Order.

When this setting is turned on, Approvers must check this box on Invoices that do not match Work Orders before they can approve the invoice.