Yes, that's right, a measured blue shift in the direction of motion relative to the 'rest frame' of the CMBR, and a commensurate red shift in the opposite direction.

Regarding the use of the term 'absolute': having scanned a few discussions on the topic in other forums, I've decided not to dwell on it. It's not worth letting my tea get cold smile

"Time is what prevents everything from happening at once" - John Wheeler