Actually those are what's called "open tugs," not Tillbury. The tug loops on Tillbury and French tugs (the real ones, not some I've seen by that name on mini show harnesses) snug down around the shaft like a slip knot when you tighten the overgirth and may safely be used without breeching for shows. Open tugs like yours are regular tug loops with a strap attached to the side or bottom that buckles into the overgirth. Their purpose is to allow the shafts of a well-balanced carriage to float in the tug loops so that bounces and jolts don't transfer to the horse via the girth and saddle. WITH BREECHING this is a very safe, comfortable style of harnessing. The traces pull the carriage forward, the breeching holds it back off the horse, and all the tugs have to do is hold the shafts up and keep them from flipping up in an emergency. The horse gets to float easily along in the middle of this balanced system without being strapped tightly to the cart.
However without breeching this tug style would be very dangerous. Even with tug stops it's quite possible for the shaft to slip forward through the tug loop and allow the cart to run up on the horse's heels which is likely to cause a terrible accident. Don't take chances- use breeching!
Leia