The transformations (austenite to martensite and martensite to austenite) are ideally diffusionless. This means that time is not a consideration for the transformation, at least not directly.
From a technological standpoint, shape memory alloys are used as actuators, so one would like a very short response time. A lot of work goes into optimising these alloys and the 'training' (prior heat treatments) that facilitates the shape memory effect. As such, there may not be a direct answer to your question. For a specific alloy, you may find something in literature, or you may need to do some experiments.
From a scientific standpoint, strain rate could have some indirect effects. Many alloys that form martensite also form twins under deformation; the two may be seen as competing mechanisms. Twinning is more prominent at higher strain rates. Therefore, martensite formation and the shape memory effect could be inhibited. Keep in mind though, that this can vary vastly across different alloys.
the question is an interesting one and actually under currrent research. Several groups have started to resorted to ultrafast time-resolved measurements to follow the structural changes in shape memory alloys. We speak here about picosecond or subpicosecond timescales which are needed to resolve the initial onset of the transformation. I will add you some papers that should help you to delve deeper into the topic.Unfortunately I can not help regarding the strain rate effect on tranformation temperatures but I hope other people can fill in.
Article Picosecond view of a martensitic transition and nucleation i...
Article Defect effects on spatiotemporal evolution of photoinduced m...
Article Collective Modes and Structural Modulation in Ni-Mn-Ga(Co) M...
This transformation is diffusionless as Mr Aashranth said. You can calculate the time of the transformation from DSC curves, by the starting and finishing points and heating/cooling rate that you have choosen.