Barbara: She's a member of the church of favonius. Fairness is written all over her job.
Mona: She's an astrologist that can effectively read a person, her relation to justice is that nobody can lie to her.
Childe/Tartaglia: While he himself is a Fatui Harbinger, his relation to justice is how he treats his job and his promises.
Xingqiu: His entire character revolves around justice and fairness.
Yelan: Her association with justice is her occupation. She easily deals with criminals thanks to her connections and many identities.
Kokomi: Her association with justice and fairness is her participation in the Vision Hunt resistance.
Ayato: He is the Yashiro Commissioner. Need I say more?
It appears that Hydro's criteria for granting Visions seens to be ties with justice and/or fairness.
