Centaurus, I am lucky enough to own and fly a Tiger Moth. Unfortunatly I cannot give you the technical explanation for the starting routine. However this is what I was taught, and it works every time. Check fuel on, then tickle carby until full. Fuel will run from drain pipe, wait until the flow stops. Check switches off and turn the prop eight blades back and four blades forward. Turn rear cockpit switches on and front switch front cockpit. Then start by pulling the prop downwards in the forward direction. Strongly suggest you get someone who has done it before to show you how to position yourself and how to hold the prop during this operation. This is the cold start method. When the engine is warm, it will start without the priming action. It is generally warm enough when you can feel it with the hand close to a cylinder.
One final point, when pulling the prop forward for four turns you should hear the impulse coupling on the right magneto make a distinct clicking noise. If you dont it will not start, a gentle tap on the maggy will often do the trick.
Remember this is hi tech stuff!!! Enjoy the flight there is nothing better. As my instructor told me, the Tiger is an easy aircraft to fly but a difficult aircraft to fly well