Commercial-grade dumortierite is correctly known as dumortierite quartz. This is because it's quartz, heavily included with crystals of dumortierite.
The abundance of crystals within the quartz is the reason the stone is opaque.
Dumortierite quartz tumbled stones are graded according to purity. Material with inclusions of other minerals, as well as dumortierite, is given a lower grade.
Different colours or markings often enable other minerals to be identified.