In IS Boxer toolkit, if you click on any of your character sets (top pane), it will list the slots (with toon name under Slot number) on the bottom left.

If you click on the 1, 2, etc.. it will tell you which mapped key is run on a character switch.

I've gone and changed mine, with a different mapped key for each Slot leading.
So I have Slot 1 is Leader, Slot 2 is Leader etc.
But you could modify an existing key quite easily or make your own if you want to leave the existing mapped keys the same.

If you look under Control Keymaps, the on a switch mapped keys are listed here.
Let's say you create a new one.
Left click on Control at the top, then right click on Mapped Keys in the left (bottom) pane.
Call it something like On Switch.

One Step is fine, as we want the same thing to happen on each character change.

Click the 1 under Steps, and then right click on Actions in the right pane.
Choose Keymap Action >> Do Mapped Key Action.
The first one will be the default move that was previously listed under the "on switch run this mapped key".
For me that was JambaMaster, but could be Follow/JambaMaster or whatever.
So now the new key does everything the old key used to.

In addition, add two more Do Mapped Key Actions.
Have it run CTM Off, for the Current Window.
And have it run CTM On, for the other windows (All Without Current).

My CTM On and CTM Off mapped keys are both set to Current Window as their target.
So when CTM On is run, in the current window it applies to the current window (active character).
When my CTM Off is run by the (active character), the mapped key is run in the windows of the non-active characters and applies to their window (the current window from the perspective of the mapped key).