Amphiphilic diblock copolymers can spontaneously form integral asymmetric isoporous membranes by evaporation-induced self-assembly. The critical structural evolution steps occur within the first hundred seconds after solvent casting. By using synchrotron X-ray scattering employing a specially designed solvent casting apparatus, we were able to follow the kinetics of the structural evolution in situ. At an initial time of 20 s after solvent-casting we observe the first structural features on length scales d of 30-70 nm, signaled by a weak maximum in the low-q region of the measured scattering curves. During the subsequent period the length scales increase continuously until after around 100 s they reach a plateau value d(infinity) of 80-120 nm, the size depending on the molecular weight of the block copolymer. Interestingly, the time evolution of the characteristic length scales follow a simple exponential saturation curve for all block copolymers, irrespective of molecular weight, composition, and addition of ionic additives, in agreement with theoretical models on two-dimensional ordered block copolymer domain formation. In addition, we could show that immersion in water during solvent evaporation leads to a nearly instantaneous increase of the characteristic length scale to its plateau value. The addition of salts such as Cu2+ leads to compaction of the structures with smaller characteristic length scales, but still following the same kinetic evolution.