You're rewriting history. When he asked for asylum Assange was only seeking refuge from being questioned on Swedish soil about the rape allegations from 2010. When he was granted asylum however, he breached the bail conditions from the UK and there were indeed two governments after him. But, I repeat, no espionage/computer charges were known until 2018.
He assumed, and rightly so, that the US government was after him. Otherwise he wouldn't have stayed in the embassy past the charges in Sweden getting dropped. It is immaterial if the indictments were known or even already existed.
For me there's a slight nuance difference between being a fugitive from "official prosecution" by the US and being a fugitive because "he feared" prosecution. The US government had official communication when he entered the embassy that he is not on their wanted list.
