There is an exponential demand for high-temperature shape memory alloys (HTSMAs) in aerospace, automotive, and energy sectors, where operational temperatures exceed 400 K. Group VIIIB transition metals provide pathways to stabilise or modify the B2 compound formed with Ti at near-equiatomic compositions. However, a core challenge remains balancing structural stability with martensitic transformation. In our previous study, TiNi, TiPd, and TiRu alloys were characterised in as-cast and annealed conditions. X-ray diffraction (XRD) and optical microscopy were used to confirm the coexistence of B2 and secondary phases in TiNi and TiPd alloys, whereas the sole B2 phase was retained in TiRu. These results highlighted that under equilibrium conditions, B2 TiRu remains stable upon cooling to room temperature with no phase transformation. The current study investigates the phase and microstructural evolution of the aforementioned alloys when subjected to solution-treatment followed by rapid cooling (quenching). Deployment of a non-equilibrium thermal process is aimed at promoting diffusionless phase transformation in which the metastable martensitic phase is induced. XRD analysis is conducted to reveal the resulting crystal structures, whereas the scanning electron microscopy (SEM) equipped with energy dispersive spectroscopy (EDS) is used to track microstructural changes as well as to determine the compositions of the phases formed. The findings of this work shed light on making a distinction between low-temperature phases formed under equilibrium and martensitic phases induced through a non-equilibrium heat-treatment process, such as rapid quenching. These insights are critical in the development of shape memory alloys.