Let's cover some fundamental principles.
Any kind of culture builds acid. Acid is necessary for proper cheese texture and flavor. When too much acid builds up, that coagulates the milk.
Rennet also coagulates milk, but not in the same way acid does. Acid precipitates the protein by neutralizing the charge the proteins have in milk. Whereas rennet is an enzyme, and breaks that protein to allow the individual proteins to bond together and form a curd.
The combination of the rennet and the acid is what makes a cheese like feta possible. In feta, the rennet coagulates in the beginning, when little acid has built up. Then as you cook the curds, the acid keeps building, and then you drain the whey off and let the curds fuse together in a mold. In the meantime, the acid builds up some more, and forms the flavor, texture, and consistency of feta. A substance called a lipase also is necessary for feta. It gives it that sharp feta taste. Lipase breaks down fats, that's where the flavor comes from.
Now in your case what happened is you added the yogurt, and let the culture make acid. It kept making acid for a long, long time. And instead of making acid in the finished, cooked, and drained curds, it made acid in the entire milk. So while the rennet coagulated the milk, it didn't really matter so much, because you didn't cut and cook the curds.
Does that make sense? Also, feta needs a mesophilic culture, like buttermilk, and also needs lipase.