Flyback Transformer Saturation in Secondary
Saturation is a function of the core (there is only one core, and it links primary to secondary winding(s)). In the case of a flyback converter, energy is stored in the core and then released to the secondary. Saturation is thus only a function of the primary current, since there is no secondary current (the rectifier is reverse biased) when the magnetic field reaches the peak value. 

In the general case, saturation would be related to the signed sum of the ampere-turns of each winding (each affecting the magnetic flux in the core), but that's not a factor in a flyback.