Glad to hear it!

Some advice for helping you get on the right foot at the right time while maintaining balance:

It is typical to slow down toward the end of the runaround to release some of the pull pressure caused by centrifugal force and prepare for the exit. I assume your partner is doing this, but if not, you might suggest it.

To achieve any kind of noteworthy speed on the runaround, it is necessary to dance it with one of the partners (typically the leader) at the center of the turn, while the other partner (typically the follower) runs around him. However, at the end of the spin, when you are slowing down, this is no longer necessary; You can run (or walk) around each other, or even exchange roles and have the leader take the outside of turn. This is especially useful for establishing your weight on one foot while you prepare for the exit -- Something you wouldn't be able to do if you were constantly changing weight because you're still on the outside of turn.

Either way, by the last beat or two, you should have enough leeway with the position (especially in a loose alternate hold) to both have a moment turning over one foot.

As a student, the more time you have to establish your weight over one foot (while still turning at the end of the runaround), the better. Your teacher, having more experience, should be able to do this in much less time. Therefore, taking him to the outside of turn at the end is a helpful tactic. He will be able to diminish the amount of time he spends on the outside of turn as you improve. But it's a good starting point to ensure that you are always balanced and ready for that exit.

Regards,
Jonathan