Let me first say welcome, Justin. Glad to have your participation on the web site.
To answer your question, the location of the right foot in the downswing is often a reaction to the function of the hips, and the players lower body center of gravity.
This might get a little complicated, since there are so many variations to this component and why it happens, but I will do my best to simplify this without losing accuracy in my response.
Basically, the right leg can be one of two things in the downswing: straight, or flexed. This becomes important because it can really be a result of how the student moves his hips. The hip girdle does two things: it rotates and it moves forward. The hips can move backward in the downswing, but that is very detrimental to most players and is a key component I find in most slicers. The hips move back and the plane line of the shaft has no where to go but left, so the entire swing plane switches from square to the target line to left of the target line. To see what I mean, you could get in a address position, and try to move the zipper of your pants over your right foot. Trying to keep your hips in the current location and making a super slow motion swing, you will find it nearly impossible for the club to approach the ball from the inside, or even square. The body and club have simply run out of room to get the club on a proper path.
To get back to the correct functions of the hips, again they rotate and they move forward. Take a look at Tiger Woods. When you watch Tiger swing, the first thing you will notice is that his hip girdle NEVER moves backward, even in the backswing. As a matter of fact, the vast majority of great ball-strikers throughout the history of golf have moved their hip girdle slightly FORWARD in their backswing. Hogan, Snead, Player, Nicklaus, and even Tiger. This position allows the lower body center of gravity (henceforthe referred to as COG) forward, which allows room for the right elbow to get more in front of the body, closer to the navel, in the downswing. This will help sustain the lag in the clubshaft and deliver the club to the ball from the proper path. You might notice that if you practice this component in slow motion, your right leg wants to straighten, which is ideal. As a matter of fact, if your hip girdle continues to move slighly forward in the downswing (which it should do), your right leg will want to remain straight into the downswing, and your right foot will want to roll onto the inside of the foot, but the right heel will remain down. Then, as the body completes the rotation into follow through, the right foot will be rolling inward and onto the toe as a reaction of the body rotation, never forced into that position.
When you see a players heel off the ground, it is often because that player's hips have moved backwards in the downswing, or the hips have over-rotated. In either case, its usually bad news for the average player. Tiger Woods has model footwork on most of his controlled shots with irons and fairway woods, try to copy what he does. I use his as an example because he is the player that we see the most, obviously.
Hope this adds some clarity, if not, please feel free to post another question or ask for further clarification.