I observed that in the current version, the mean of the quality values at each read position is identical between first and second read. This is not the case for the reads I used to train the quality distributions. This happens for all tested datasets.

I trained the distribution with:
baseCalling_Matrix_calculator -m 42 -r ref.fa -i reads.bam -o baseCalling

And included it during the simulation with
-B baseCalling.count.matrix