It's hard to say why Watson translated it that way. The Latin is unambiguous. Indeed, it's "from Europe (ex Europa) (in)to Asia (in Asiam). I checked the Budé edition, and there's no note indicating an alternative reading from the manuscripts.
I'd probably just chalk it up to a mistake, although he might have been "correcting" the text, since immediately after this Persians are back in Greece to capture Eretria. It is possible he misunderstood the sequence of the action.
Then again, it might just be a typo, too, as just a little bit above you see the following typo: "Miltiades, in consequence, exhorted the guardians of the bridge not to lose an opportunity, presented them by by fortune."