Just to make sure, I understand the issue correctly:

if you train 4 models sequentially as A, B, C, D, you get exactly the same results for different runs
If you train model A only, you will get exactly the same results for different runs
if you start with model B, the result will differ from the other runs (e.g. from A, B, C, D)

Is that correct?
If so, the difference might come to another sequence of calls to the pseudo random number generator.
If you are seeding the code, the PRNG will generate the same “random” values for the same sequence of calls with the same arguments.
However, if your model definition of model A differs from model B (e.g .different number of hidden units in a linear layer), will will not get the same results.