It's quite normal at first and one of the trickiest aspects of subtone. Once you've got to stage one of being able to do it, then work at it to get the subtone less flat.
A good exercise is to play long notes going from subtone to fulltone (is that the right word for non-subtone?) and back keeping your ear on the pitch.
Also I am in the habit of now tuning slightly sharp. This means I get in the habit of a more relaxed full tone and easier to match the tuning with subtone. Also playing a bit sharp is not such a bad thing as playing flat (Didn't do Charlie Parker any harm).
Tuning a bit sharp also helps with vibrato as there is a tendency for vib to soud flat because the pitch is usually lowered as you vib.