@Michael ********
Your flight to Saigon is the perfect proof of onward travel, as the airline flying you to Thailand will want to see a proof that you leave Thailand within the 30 days stay permit, you will get stamped in upon arrival
Immigration generally rarely asks for proof of onward travel. This question is reserved for offenders of multiple consecutive visa-exempt entries.
For the flight back to Thailand, your return ticket to the U.S.A. is, again, the perfect proof of onward travel within the next 30 days stay permit.
Keep in mind, PRINT all the tickets on paper. Most check-in staff will thank you!