I'm confused about your generator. Is the 30 amp outlet a 3 or 4 prong unit? With the TT jack OR a twist lock three prong jack, you have one hot, one neutral/return and one ground. Where is the 240v coming from, is it a welding generator?
A 30 amp clothes dryer plug has two hots and one neutral, hence most dryers have a separate ground wire to be attached. These are for 220-240VAC across the two hot wires.
On my generator, if you measured from the hot to ground, you get 120VAC. If you measured from neutral to ground, you would get 120 VAC. This not from two separate supplies, but from each side of the generating coil, one would read negative and one would read positive. So 30 amps total, at least on mine.