I have turned Alabaster and will not soon try it again. The pens came out great but the mess the dust creates is not on my favorites list.
I turned it at a medium speed, good vacuum and a fan to blow clean air into my breathing area while wearing a mask rated for fine particulates.
The shop was white when I got through.
I believe the dust from the Alabaster contains silica and therefor makes it far more dangerous than originally thought.
If I did it again, I would set up two fans, one on either side of me, to blow all of the dust away from my breathing area, and try to trap it in a box with a filtered vacuum set up.
You may find the effort worth it. I have a friend who turns goblets and uses water to keep dust in control. My nephew has several Alabaster mines and he has no trouble cutting it (Outdoors). Use sharp tools and expect cracks and an occasional explosion. Face shield a must.
Good Luck and post photos.