I believe they use a combination of hydrogenated oils, yeast and standard leavening agents like baking powder and baking soda.
My experience is that without hydro, the super rising crusts are just tougher to make. I have settled for a medium riser but an awesome taste. I like to use yeast in my pizza crusts. Generally, chemical reactions go faster at higher temps, so yes temperature does matter...
However, since the reaction starts immediately, I would say it is more dependent on the amount and how long you let it work. The trick is the optimize the timing so that you bake the shape you want (i.e., fluffy and big) into the crust just as it gets to that point from the leavening (the most risen and fluffy). If you wait too long it will depress...
I read a bit about this here as well:
http://en.wikipedia.org/wiki/Baking_powder
The way you describe it, it sounds as if your oven uses microwave radiation while you are baking the pizza. This is obviously a bad idea, but a manufacturer could just add "pizza setting" as a selling point, without making a reasonable implementation. Or maybe the oven is OK, but the user interface is confusing and you somehow don't switch on the right setting.
First, try to find out if the oven is supposed to turn off the radiation while baking pizza. If this isn't described clearly in the users' manual, call technical support and ask them. If it is not supposed to turn it off, your last chance is that the oven has the possibility to manually override the setting and turn off the radiation. Else, this oven is not suited for pizzas or any other kind of dough.
If the oven is supposed to turn the radiation off, and you are sure you have selected all the correct options for it to do so, but your crust is still too hard, then the oven is probably defective and radiates microwaves when it shouldn't. Sadly, I don't know any way to test for that (theoretically, you could put a small piece of metal in it and look for sparks, but you risk damaging the oven that way.). Maybe if you have a friend with access to a physics or a sepcialized photography lab, they could find you some microwave sensitive film, but the probability is slim.
If you somehow find out that the microwave definitely isn't nuking the pizza, the only other problem I can think of is that it probably gets too dry when baking. You could try baking a thicker pizza (put two pure bases on each other and roll them a bit with the rolling pin, they should combine) and/or adding more sauce and fluid toppings/cheese. Or reduce the baking time. But it would take a lot of drying to make the crust unpleasantly hard, so I am 90% sure your problem is caused by microwaves.
Best Answer
It's possible to make a good pizza on the stovetop (with a lid), but it won't quite have the same consistency as a New York style pizza.
Serious Eats had a write-up on 'skillet pizza' years ago.
Basically, the idea is that you cook the crust first in the skillet, flipping it twice (so the flat side is on the bottom again), then top it and put a lid on it to melt the cheese ... which should work pretty well in your tandoor.
A few words of advice :
I actually use this method even when I have an oven, especially when I'm cooking for a lot of people -- I cook the crusts on both sides on a cast iron skillet or griddle, then move them to a sheet pan and let people add their toppings, then put them in the oven to melt the cheese.