It sounds like you might have a wood to metal tube glue failure but there are several possible problems. It is a fact that cross cut wood is weaker than longitudinal cut wood. Weak by far, but much more interesting in my view so well worth the effort to figure out your problem.
Is your glue failing? CA does not always work well with every porous woods like Zebrawood. I use gorilla glue with well roughed up brass tubes to bet good wood to brass bonds. CA and even epoxy glue joints can be weak if you do not get even coverage and good penetration of glue. CA can setup with voids and very shallow penetration into the wood. Epoxy can fail if you do not get complete and even coverage of glue. Gorilla glue is an expanding type glue which expands and penetrates as it sets. Minor voids may be filled by this action. On really weak, punky or porous wood I flood the hole after drilling with thin CA. It both reinforces the wood from within but also gives the glue, whatever type you are using, a good surface to bond to. Gorilla glue bonds nicely to CA reinforced holes.
Second question is how sharp are your tools. Dull tools catch quickly in soft woods and have a tendency to rip out chunks of grain. Crosscut wood has very little strength because you are only relying on the cross grain inter fibers for support to hold the blank together. Soft, open grained wood with a lot of pores tend to have very few inter connections and tend to be brittle or break easily with side pressure.
Third what tool do you use to turn with? Gouge or Skew? With cross cut Zebra wood I use a scary shape gouge for 90% of my cutting. then finished with a scary sharp skew. Very light pressure is required also. When done right your shavings or chips will be less than paper thick. Soft woods do not respond well to anything but a very light touch.
Four, if tools are not scary sharp you are fighting a uphill battle whenever you turn cross grain blanks. You can sand a blank to shape if you want but the level of precision and control you have leaves a lot to be desired. I can turn a pen to .001-.005 with hand tools but would be lucky to get to within .010 with sand paper. Flap sanding refers to one of those flapper sanding heads like we used to use in a drill to clean paint off a metal surface. You could rough shape the blank with one of those and try to finish with chisel but I loathe using a good metal chisel to turn wood after I have impregnate the surface with a nice abrasive grit.
Five, it might just be a problem with the wood you are turning. Zebrawood is known for small internal voids and hard gum like inclusions. Perhaps your wood is just very weak by nature. Frequent coating of the wood as you turn it will give it some strength and the glue will fill in any minor voids in the wood which should make it stronger and less likely to blow up.
