Many applications of responsive microgels rely on the fast adaptation of the polymer network. However, the underlying dynamics of the de-/swelling process of the gels have not been fully understood. In the present work, we focus on the collapse kinetics of poly-N-isopropylacrylamide (pNIPAM) microgels due to cononsolvency. Cononsolvency means that either of the pure solvents, e.g., pure water or pure methanol, act as a so-called good solvent, leading to a swollen state of the polymer network. However, in mixtures of water and methanol, the previously swollen network undergoes a drastic volume loss. To further elucidate the cononsolvency transition, pNIPAM microgels with diameters between 20 and 110 mu m were synthesized by microfluidics. To follow the dynamics, pure water was suddenly exchanged with an unfavorable mixture of 20 mol% methanol (solvent-jump) within a microfluidic channel. The dynamic response of the microgels was investigated by optical and fluorescence microscopy and Raman microspectroscopy. The experimental data provide unique and detailed insight into the size-dependent kinetics of the volume phase transition due to cononsolvency. The change in the microgel's diameter over time points to a two-step process of the microgel collapse with a biexponential behavior. Furthermore, the dependence between the two time constants from this biexponential behavior and the microgel's diameter in the collapsed state deviates from the square-power law proposed by Tanaka and Fillmore [J. Chem. Phys. 1979, 70, 1214-1218]. The deviation is discussed considering the adhesion-induced deformation of the gels and the physical processes underlying the collapse.