You're Correct!

Ball position should vary within your stance dependant upon the club that you are using. The correct ball position, for right handed golfers, varies from the middle of your stance to your left foot and to be more exact so that the ball is positioned opposite your left big toe.

When playing your short clubs, your sand iron, pitching wedge and 9 iron, you should set up at address with the ball positioned in the centre of your stance. The ball should then move half a ball width to the left of centre for each subsequent club, so half a ball left for your 8 iron, another half a ball left for your 7 iron, until you are playing your driver from opposite your left big toe.
The ball position needs to vary in this way in order to allow you to make a strike with a square club face, which will allow you to hit a straight golf shot as the club head swings along the target line.

The shorter that the golf club is, the more upright the swing that you make with it becomes. As a result of this, the club head is swung along the target line for a much longer period of time than it is with a longer club. A longer club makes a flatter, more arcing swing and as a result it takes longer to square the club face, or get the club face aiming at the target, as the club head travels along the target line. Therefore, you are able to position the golf ball between your feet at address when using shorter clubs and still square the club face to the target at impact.

But the longer the club becomes, then further down the target line you need to position the golf ball, in order to allow yourself the required time to square the club face to the target at impact and this is why the ball moves left in your stance.

Playing the ball from the centre of you stance will work for your shorter irons, but doing this with your longer irons will give you directional issues. The club head will impact with the ball before the longer club has a square club face to the target and as a result, you will strike the golf ball right of target with your longer clubs with this ball position.

Playing the ball from just inside your left foot will allow you to play accurate shots with your longer clubs, but with your shorter clubs you will tend to hit shots left of target with this ball position. The club face with shorter clubs is square, or aiming at the target, by the centre of your stance. Striking the ball after this position would result in the club face rotating left of target before impact and as a result, the ball will fly left of target.

Playing the ball from your back foot will result in you striking the ball to the right of the target as the club face will be aiming that way as you connect with the ball. However, you will also be swinging the club on your down swing and as a result, the club face will be delofted at impact and you will also experience the club connecting with the top of the golf ball. This will produce a very low trajectory shot.