Go ahead and stress test the distance, you'll be surprised.
As of the last update I was running biters at 7 chunks, so ~224ish tiles. It gets to the point where you couldn't see the limit without placing from the map. I would alternatively suggest it is a "out of range" popup on the placed field office itself, for instant feedback on placement.
Side note for notifications, the "no power" popup on the field office only stays for a moment before disappearing, making an unpowered field office look like its just out of biter range instead for a new player.
And yes, an updated tooltip :v