In the screenshots provided my primary hero (Fasol Staccato) assigned to my home system is providing all of it's system resource bonuses to all Sancturaries in the empire (which is then collected by my home system). This means that all system bonuses from that hero are multiplied by each system in the empire causing very high FIDSI generation.

https://imgur.com/a/tjZr5jW

This effect stacks too, in combination with my other bug report multiple heros with system resource bonuses I am now getting almost +200 science for every sanctuary thanks to 2 hero's with the Blue Sky Speculator skill!