Suppose you hit the throttle and the car starts running. Two things can happen:
1) the standard 2-speed shifts from 1 to 2 and then (later) the 2-speed on the spur shifts from 1 to 2. So two gear changes, as you said.
2) the second thing that can happen is just the other way round: spur shifts from 1 to 2 and later the standard 2-speed shifts from 1 to 2.
What will happen in practice depends on the shifting points.
So, the four opions are:
1) standard 2-speed in gear 1, spur 2-speed in gear 1
2) standard 2-speed in gear 2, spur 2-speed in gear 1
3) standard 2-speed in gear 1, spur 2-speed in gear 2
4) standard 2-speed in gear 2, spur 2-speed in gear 2
I agree that you can made a 3-speed with this setup, but only if you set the shifting points correctly. If not, you will end up with a very unstable 4-speed.
OK, enough argueing for today...