Maybe im not making this clear so.
In bw1, the whole egg rng process is initiated real-time by the main Pidrng, while MT rns are only separately called when unibherited ivs come into need.
Bw2, the seed of the rng is no longer a frame of the main pidrng, but derived(the article didnt explain how) from 2 calls of MT when the previous egg has been taken. This seed does not change until the rng process is initiated&completed when the egg is generated. Everything except pid is derived from this seed and its subsequent frames, including the uninherited ivs. The pid is determined later when taking the egg, by the main pidrng.
Xy, the seed still appear fixed, again indicating a separate rng sequence like in bw2. The difference is that the true pid (gender, etc) and the encrypt constant is now from this rng as well.
The article's conjectures "gender is independent from pid" should be understood as "pid(=gender)is independent from the encryption constant(=spinda)", and "pid is determined last" as "encryption constant is determined last". The fact that gendered pokemon is 1 frame behind the genderless in everything else, may indicate that the true pid is the first to be determined in the process.