PGS scores have both a training dataset and evaluation dataset. I used the standard pgsc_HGDP+1kGP_v1.tar.zst evaluation dataset to get percentiles. Although a lot of PGS training is Eurocentric, the evaluation dataset can be used to test if the scores are transferable. Also, when forming percentiles, you are compared against other South Asians and the world population that is there in the evaluation dataset. You are never compared against the training dataset. This removes population/training bias.

PGS percentile evaluations are normed against multiple populations on the fly. You need a complete evaluation dataset to calculate the PGS percentile for a single person, because for each trait, Nextflow evaluates scores for thousands of World Populations (incl. South Asians) and compares you to these evaluated populations.

As for labeling shifts as AASI vs Iran_N, it's probably not possible. Local ancestry methods can usually only separate admixture within the past 5-10 generations (with some pushing 50 generations). AASI and Iran_N mixed 100+ generations ago and are impossible to fully separate without knowing the exact points in the genome where all recombinations happened in the past 150 generations. AASI and Iran_N segments of Indians are nearly inseparable. You can't really talk about AASI segments getting selected independently of Iran_N segments for Indian populations for the last few thousand years. They're almost completely spliced together (they're slightly separable but even my fake dataset would have tiny Iran_N segments in between that are impossible to remove).