. Does anyone know more or less arrived when the kroot arrived in the koronus expanse? Was it before or after the Imperium discovered it?

Probably after, but there's no particular fluff about it.

Most likely before. Kroot travel via Warspheres, or carried via other races as Mercs. Since its said the gate which connects the Eastern Fringe with the Koronus Expanse has just recently been activated and as soon it was discovered the Imperial Navy blockaded it. However like Orks the fluff says Kroot aren't too far behind.

Per the Deathwatch fluff, the warp gate was discovered by the Imperium in 755.M41, and it was already active at that point. The Kroot could have transited the warp gate before the Imperium found it. The current year is, what, 816.M41? So, the Kroot have probably been in the Expanse for at least 60 to 70 years.

Cheers,

- V.