Here’s what I can tell you. ALL GREEN wood will warp and change dimensions some. Some woods like mesquite do so only a small amount after it is dry, but all woods shrink and expand with the humidity and temp. .
What I recommend for pen blanks s that you cut your green wood into oversized pen blanks then quick dry them in the microwave. To do this you put the cut blank(s) into the microwave and cook on high for 1-2 mins. Then let cool and allow the water vapor to transpire. Then cook another two mins or so and allow it to cool again. After several iterations check the water content with a meter. If it falls within limits say 10-15% depending upon the wood then you can turn it just like it was kiln dried.
You can cook them in a conventional oven, too although I’ve never messed with doing so. Some woods tolerate high power on the microwave better than others so if you’re nervous about cooking them use a lower power level initially,
You can’t do this with very large pieces of wood but it seems to work fine for pen blanks.