This is very interesting to me and I hope the OP will update us on what he finds out.
We, too, have the TST507 (non-flow-thru) set up. I recall that when we first started using them on our TT and Exploder, we pulled into a campground, unhooked and set up and then headed off. We were several miles away from the TT when we realized we were still getting a reading from the TT's sensors.
Since we were in Tampa for the RV show, I took the monitor (still showing the TT's tire temp/pressure readings) to the TST vendor there. He showed me something I had done wrong in the set-up, but for the life of me I can't remember what it was. User error in my case.
That being said, I do wonder how adding a repeater would have helped in the OP's situation. Without one, the sensor reading should have dropped and after five minutes there should have been no reading on that tire and alot of beepage to indicate that the signal had been lost.
Obviously we've not seen a photo of OPs tire after the blow-out, but it isn't likely there was enough air left in the valve stem to produce a reading unless they were the airlock/airless variety?
Also, it would be nice to know if the the OPs TST sensors were flow-thru or regulars.