Thanks for the pattern link. It’s easier to know what you’re following.
The sleeves are sewn in so your bind off under arm and the edge stitch of the whole sleeve cap is going to be taken into the seam and not be seen, therefore the colour work on those few bind off stitches under the arm won’t be seen. You can follow the colourwork chart, adding in the colour as the chart shows for all the stitches if you want to but personally I wouldn’t.
I find it nicer to seam if I have a single colour and a sturdy bind off edge.
If you want the colour work included in the bind off edge you need to think ahead for each stitch. Stitch 1 is bound off over stitch 2 and needs to therefore be the colour of stitch 2. Stitch 2 binds off over stitch 3 so needs to be worked in the colour of stitch 3. And so on. For the underarm which is seamed I just wouldn’t bother. I have done this colour work where I have had a colour panel, intarsia or 2 colour neck band for example which is a bound off edge which is visible and therefore I wanted the bind off to match the colour change.
To match up the rest of your colourwork after binding of and for the rest of the cap you will need to read your work and check where to start each row on the chart. Drawing on the chart could help and you can follow the co,our an shaping I one go. Another way is to put a marker in at a central stitch and on your chart and work outwards from there to check each row begins with the correct colour.
If I am not answering the question you asked (I might have misunderstood the problem) do say.