We develop here a microfabrication compatible force measurement technique termed as ultrasoft polydimethylsiloxane-based traction force microscopy (UPTFM). This technique is devised for mapping the cellular traction forces imparted on the adhering substrate, so as to depict the physiological state of the cells surviving in the micro-confinement. We subsequently integrate the technique with a microfluidic platform for evaluating different states of stress in adherent mouse skin fibroblast L929 cells. Utilizing this technique, we monitor the spatio-temporal evolution of cellular traction forces for static incubation periods with no media replenishment as well as for dynamic flow conditions that inherently induce cell deformation and detachment. While the studies conducted on a quiescent fluid medium enable us to obtain an optimal static cell incubation period, those executed under dynamic flow conditions provide us with the minuscule details of the cellular response, deformation and detachment processes. We elucidate the correlation between shear activated cytosolic calcium ion release profile and the local traction forces as an attempt to apply UPTFM in the domain of functional biological purposes. Pertinently, we map the centroidal displacement and the maximum traction stress in characterizing the critical shear rate conditions for the onset of the cell peeling-off process, and demonstrate their contrasting features in comparison to the vesicle lift off processes in a shear flow. Theoretically, these deviations can only be explained by taking physiologically relevant cell adhesion models into consideration, which, while retaining the intrinsic simplicity, are able to reproduce the key experimental outcomes at least with qualitative agreement. We execute further theoretical investigations with variable magnitudes of membrane stiffness, viscosity and adhesion strength, so as to come up with interesting biophysical confluences.