James is right. Often what seems like two conflicting opinions is really just emphasis on two different aspects of the same concept. This is the perfect example of such a case.
To shed more light on the technical side of this concept, I have this to add:
When you turn on a foot there is one thing that is always true 100% of the time: You *always* turn over one part of your foot, either the ball or the heel. You will not turn if both the ball and the heel of the same foot are connected to the floor with weight. In fact, if you are turning over one part, and the other part connects and takes weight, it acts as a braking mechanism to the turn.
So when people turn on one foot and the foot is flat, it only looks like they're turning over the whole foot. In reality, they are turning over one part of the foot. The other part of the foot, while in contact with the floor, does not have any body weight.
Knowing this, what you have to realize is that both teachers want you to turn over the ball of one foot and the heel of the other. But the second teacher, seeing you fall off balance, is concerned that you may be over-emphasizing the foot action (either the heel or the ball is over-articulated -- a common cause of balance loss during a heel-toe twist), and wants you to tone it down.
In my opinion, a perfect heel-toe twist has the heel foot flat, and the toe foot semi-articulated. Actually, it's not a toe at all but a ball, because you want to get some presuure into it using body weight (let's say 20%). As the turn continues, the heel of the back foot lowers gradually until both feet are flat at the end of the turn. Ideally your feet will close perfectly together after 3/4 turn.
The best way to improve your balance and practice correct foot action on a heel-toe twist is to break it down into quarters. Begin by crossing one foot behind the other, then stop and check your foot position before continuing. Also, check your weight to make sure that you are about 80/20 in favor of the forward foot.
Turn 1/4 *only*... no more, no less. You should now have your feet in line, as if to be walking a tightrope. Front foot flat, back heel up but slightly lower than you began. Weight is still 80/20. If your weight shifted away from 80/20 (a very likely scenario in the beginning), you already know what you have to work on. If something is out of place, fix it and move on.
Turn another 1/4 turn. One foot should be a few inches to the side and forward of the other. The forward foot should still be flat, the back heel still up but only slightly, and most importantly, the weight still 80/20. If not, fix it, and then move on...
Last 1/4 turn, and this one is fairly easy. If your foot positioning was correct up to this point, the feet will close perfectly. Now both feet are flat, and you can shift your weight entirely to one foot or the other, depending on what comes next. Often times people want to do a total of a full turn, in which case an extra 1/4 turn is required at this point. For this extra 1/4 turn, the weight should be held over the ball of only one foot, although both feet should be held together and flat.
One note about this exercise: Don't be in a hurry. Stop at every 1/4 turn increment and correct your weight positioning before moving on. If you try to snap too quickly through the turn, you will retain old habits. Only through slow practice and self-correction will you be able to pinpoint and correct the loss of balance, which will most likely be found somewhere in the first two quarter turns, where your body is shifting away from 80/20.
I hope this helps.
Sincerely,
Jonathan Atkinson www.ballroomdancers.com