Google ad manager 360 - ad request discrepancy due to placing GPT tags via multiple GAMs

Question

We are running a parent Google ad manager account. There's this one other agency who connects us to publishers. They also have their own Google ad manager account. As they would like to control numbers delivered, with GPT tags we set up on our GAM, they do not pass directly to pub, they place our tags on their GAM, then give their GPT tag to pub. Pub then put agency's tag on their GAM, and finally place their GPT tag on their sites. Ad requests recorded by us and agency has a huge discrepancy. Agency record tens of thousands of requests while our report shows only hundreds. Not to mention fill rate for the request amount that reaches us is also incredibly low. Theoretically speaking, I understand that calling tags multiple times via multiple GAMs like that causes the discrepancy as at each calling, a part of requests get disqualified. But I can't explain the low fill rate. Has anyone experienced the same situation? Can you give me any advice on how to improve? Thank you very much