Baking – Why using both baking powder and sodium bicarbonate

The existing answers already explain why yeast and baking powder won't work together. But even if they did, you wouldn't have a reason to use them.

You seem to think that fluffiness depends on the amount of gas produced by the leaveners. In fact, it depends on both the gas and the ability of the dough to trap that gas. If you produce too much gas (no matter whether through yeast or through baking powder), then the fluffiness will be less than when using the optimal amount of leavener. This happens because your dough cannot hold the gas and the bubbles break, resulting in the dough deflating like a punctured tire. So even if combining two leaveners would have resulted in more "blowing big" action (which it doesn't, see the other answers), you would not end up with a fluffier end product. If you want fluffy muffins, you have to use a recipe and a technique which is best capable of retaining the gas produced by the baking powder. The amount of gas production is not a bottleneck.

The short answer to your question is YES. The extra acid in the ingredients will hamper the second act of the double acting baking powder. The acids are timed/staged for reaction not the baking soda.

The Magic Baking Powder (happens to be in our kitchen, too) is mostly a single acting formula since monocalcium-phosphate is a low temperature acid (with apparently some double acting properties due to generation intermediate step of dicalcium phosphate; per your link). High temperature acid for second acts typically include sodium aluminium sulfate, sodium aluminum phosphate and sodium acid pyrophosphate.

You can try to counteract that by adding a bit of baking soda, but you run the risk of altering the taste and not having it all neuralized.

If you really want to get pedantic, use a pH meter to measure the acidity of your dough. I suspect tasting the dough might give an indication as well. (bitter alkaline, sour acidic)

Another test might be to mix your acidic ingredients in a bowl with some water and start adding measured baking soda until you see no more reaction (bubbles) and use that as a your basic of neutralizing your dough.

All said and done, I agree with SAJ14SAJ that you'll be just fine going with the existing recipe. There should be enough baking soda left to get something out of your double act. I also heard it from a world-class baker that most recipes can be done with only baking soda, let alone baking powder or double acting ones.