I make my bedmi poori mix and store. I have never used ready-made mix, so cannot advise on the techniques needed to get soft pooris. However, I follow the following procedure for making the pooris.
The first step is to mix 2-3 tbsps of ghee or oil in the flour. The quantity of the oil/ghee will depend on the amount of the flour.
The flour consists of sooji and urad dal, among other ingredients, so you need to knead it differently from the way you would for regular pooris. I have always used lukewarm water for kneading the dough. It takes a lot of water because the ingredients absorb the water. When you soak dal for cooking or sooji for making rawa idli, the two soak water, right? The same happens when you use these two ingredients in the dough. They absorb the water, which is why you will need to use more water.
You'd need less water if you are using soaked and freshly ground urad dal for the poori. Since the ingredients are dry, the quantity of water required is a little extra.
The dough should be made soft and not hard, as you would for normal pooris - though it should not be too hard. Firm yet soft is the best way I can describe how the dough should be. Once you have kneaded the dough, cover it and let it rest for 20-30 minutes. This step is key to getting soft pooris that puff up on frying. The ingredients (especially the suji and urad dal) absorb water and become soft. Less water will cause the pooris to turn out hard.
After you have rested the dough, rub a little oil on your palms and gently rub it in the dough. You don't need to knead it with your knuckles. Just use the ball of your palms to work and stretch the dough, a bit.
Shape the dough into balls and roll out the poori. Don't use flour for rolling them out, use oil instead. Roll them a little thick; thicker than normal pooris. And, don't press down hard while rolling them. You need to do it with a gentle hand, making sure that they are of equal thickness all around. The oil should be hot when you fry the pooris, but not smoking. To make them fluff out, use the slotted spoon to gently press the sides of the pooris as they are frying. Don't press them in the middle. Incidentally, I had bedmi pooris for breakfast this morning.