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We extend the existing results on surjective isometries of unit spheres inthe Tsirelson space $T\left[\frac{1}{2}, S_1\right]$ to the class$T[\theta,S_{\alpha}]$ for any integer $\theta^{-1} \geq 2$ and $1 \leqslant\alpha < \omega_1$, where $S_{\alpha}$ denotes the Schreier family of order$\alpha$. This positively answers Tingley's problem for these spaces, whichasks whether every surjective isometry between unit spheres can be extended toa surjective linear isometry of the entire space.  Furthermore, we improve the result stating that every linear isometry on$T[\theta, S_1]$ ($\theta \in \left(0, \frac{1}{2}\right]$) is determined by apermutation of the first $\lceil \theta^{-1} \rceil$ elements of the canonicalunit basis, followed by a possible sign change of the corresponding coordinatesand a sign change of the remaining coordinates. Specifically, we prove thatonly the first $\lfloor \theta^{-1} \rfloor$ elements can be permuted. Thisfinding enables us to establish a sufficient condition for being a linearisometry in these spaces.

On isometries and Tingley's problem for the spaces $T[\theta, S_{\alpha}], 1 \leq \alpha<\omega_{1}$