please don't "tug" western either !!
With a well trained western horse, you should find that if you just shift your weight backwards (when in halt), they will pick it up and start to back up. (i.e. like a very slight lean back).
You sometimes see western riders tap the front shoulder with their foot if the horse is not reacting quickly enough - but I've only seen this rarely. Personally I prefer to stay in balance but I'm just a everyday rider...
Of course you may be riding two handed with a snaffle, or one handed with a curb ?
Say you are in walk and you ask for a halt - the rein back aids are as if you do not relax and give once they halt, but keep on asking for halt. It should not be a pull or tug - no backwards movement in the hand. Some western horses will recognise if you raise the hand(s) slightly. Just close the hand (or keep it closed) around the rein. Effectively the rein is there just to prevent forward movement, not to make any backwards movement.
Shift your weight back slightly and apply a light leg. If the horse does not respond, you can bump him slightly with your leg. But don't bump with the rein - just keep a 'holding' feel.
As soon as the horse steps back, lighten the rein contact and open your hand. If you want more than one step, and the horse stops at this point, close your hand and 'hold' again, and reapply leg pressure. But as your horse gets tuned in, you should find your weight aids are enough to sustain the back up without more leg and hand.
One final thing - it is really useful to establish that your horse knows HOW to back up by doing it from the ground first ! Use a gentle pressure on the nose, or on the chest, to ask for a step back. Again reward as soon as the horse responds. Once they get the idea you can keep your hand in place but with very little pressure and they should start to take more steps.
So check they understand about yielding to pressure like this and THEN get on and do it from the saddle.