I have a AJS Regal Raptor DD125E. When I push the starter switch the engine spins but no spark at the plugs. However as I release the starter switch I get a spark from the plugs on the engine overrun.
I had a similar issue on a car years ago, has the feed to the ignition been put on the wrong terminal? i.e. one that is not "live" when the starter operates? if so, then it causes exactly what you describe. One way to test is to supply the ignition circuit directly from the battery and operate the starter, results will be evident.
Sounds like the ignition or starter switch is the problem. The switch should be leaving some circuits hot in the crank position. It's also possible that the starter is pulling the circuit voltage low enough that it's not sufficient enough to fire the plugs. Check you battery, and connections as well.