I use bloodwood often and yes it does catch and crack like that. I have two carbide toothed 4-bladed mills and they will do that. While it can be your mill, it is a characteristic of bloodwood, which is brittle of sorts. A note - in using pen mills, make sure you are using the blank vise to hold it. A vise holds it steady; holding by hand is for doctor visits, or at least band-aid usage.
What needs to be considered is the "way around" this, if you are having trouble. I do have a saw jig in which I can safely cut the ends to within around 1/64 of an inch of the tube - to get it close. After that I use a sander.
Sanding down to the tubes is the best solution and can be done in two basic ways:
1. Manually on a sander, or a sanding jig to square the ends up.
2. Lee Thomas (firefyter) makes a "sanding pen mill" in which adhesive backed sandpaper is used. You can reverse the cutter head on your pen mill and use the flat back side this way. Just add a small adhesive backed piece of sandpaper to the mill in this configuration and sand it smooth.
This takes a few minutes longer, and as long as you are not in a tight production schedule, works great.
Here is a link to an ebony segmented pen in which the ends were sanded down to the tubes, and ebony cracks just like the bloodwood does with pen mills (DAMHIKT):
http://www.penturners.org/photos/images/940/1_Best_pen.jpg
When doing a nice pen, it doesn't hurt to take extra time to get the "just right" fit and finish.