Ah, I think that I understand.

Basically, the half old color/half new color sc and the sl st *replace* the first two stitches of the round.

So, if a "regular" pattern told you:

Round 1: sc 12

Round 2: change color, sc 12

then, with my method, you would do the following instead:

Round 1: sc 12

Round 2: pull through a loop as if to start a sc, leaving two loops on the hook, change color, pull yarn through both loops on hook, sl st 1, sc 10

Hope that helps!