You have asked enough questions on the subject of Vow of Poverty to know how this is going to go: Book of Exalted Deeds is rather unclear, and all available commentary on the subject is basically “if you have to ask, the answer is no.” Vow of Poverty is poorly written, poorly considered, poorly designed, and should never be used—this glib kind of short-shrift given to corner-cases is perfectly consistent with the writing of Book of Exalted Deeds on the subject. By that metric, a storage crystal created by astral seed violates the Vow.
Rules as written, the feat says you may not have “any material possessions,” with only a few exceptions. A storage crystal is not on that list of exceptions. Is a storage crystal a “material possession”? Who knows? But again, I’m inclined to say it probably is—after all, it’s a physical object, not a psionic effect. Astral seed is instantaneous, which means it creates something that remains after the psionic effect has ended. The storage crystal would not be wiped out by null psionics field, for that matter, it even works in a null psionics field (as would a psicrystal). It’s an object. That seems like a “material possession” to me, so I would rule it as such.
You know, stipulating that I would allow Vow of Poverty at all, which I wouldn’t.