How do I know that Accounts Payable/DTS received my voucher and that it will be paid?

You can review vouchers that you have added in PeopleSoft. The navigation is the same as entering a new voucher 

Main Menu > Accounts Payable > Vouchers > Add/Update > Regular Entry) then click on the Find an Existing Value tab. 

You can search using any information you have, but the Business Unit must be UTSA1 and one other field must be populated (even if you just enter a zero in the Voucher ID). All vouchers that match your criteria will appear in the Search Results. Click on the voucher you would like to review and it will appear. (Note: If the criteria you entered matches only one voucher, then it will appear without listing the Search Results.)

Without workflow in place, these vouchers will automatically be sent to DTS for processing and payment.