intarsia join

There is nothing mysterious nor difficult about changing colours between one block of colour and another. This is sometimes referred to as an intarsia join.
The rule: OLD OVER new. Then you bring up the new yarn around the old. No twisting or any other shenanigans.

right side

Place old (grey) yarn over new (blue)

Bring up new (blue) yarn around old (grey) and continue to knit with new yarn.

wrong side

Just the same as on Right Side:
Place old (blue) over new (grey).
Bring up new (grey) around old (blue)

the bumps

This is what it looks like on the Wrong Side: simple purl-like bumps.