A few notes : "as soon as Croesus marched away"
I would go for "knowing" for "επιστάμενος"
I'm not sure what you translated as "certainly". If it's "μέλλοι" then its actual meaning is "going to", "plans to"
As for your actual question
"When he came to these conclusions", "When he decided so" or something like that would be a good translation I think. Sort of "the minute he decided to do so, he acted on it as fast as possible" kind of thing.