Tiger's eye is quartz that has grown through and replaced a fibrous mineral, keeping the fibre structure. Light reflecting off those parallel fibres produces chatoyancy — a band of brightness that slides across the stone as it tilts, the same effect that gives a cat's-eye gemstone its name.
The moving band is the identification and it is very hard to fake convincingly in natural materials. Manufactured fibre-optic glass, sold as 'cat's eye' beads in bright unnatural colours, does produce a band, but the band is razor-sharp, dead straight, and identical on every bead in the strand. Tiger's eye's band is softer, slightly irregular, and varies piece to piece because the fibres do.
Blue material is called hawk's eye and is the less oxidised form. The vivid red tiger's eye on the market is almost always the golden variety gently heated, which converts the iron to a red oxide. That is a long-accepted treatment rather than a fraud, but again, it should be said.
References and sizesBlue 'hawk's eye' · Red tiger's eye (usually heat-treated)
Establish which of these you are holding before judging it. A genuine piece read against another reference's rules will look wrong when it is not.