Piznit, they generally take the planets in their immediate sector, but not beyond that. Even the Arceans, with their speed penalty, will expand more quickly.
And they are
building colony ships.Here's a screenshot
Sorry it's small and fuzzy, but you can see that there are four Drengin colony ships parked on Drengi. And while their home system is in kind of a lonely spot, they have tons of scouts roaming around (as the AI always does) and have had ample time to secure some of the planets to the south and west.
The Yor have the same problem. Heck, they failed to colonize a planet one sector away before the Krynn beat them to it from six
sectors away. How many colony ships orbiting their homeworld? Five.
Notice that even the Arceans, who truly are in a lonely corner of the galaxy and
have their natural speed penalty, managed to secure some planets during the rush.
This has happened on three different Immense games. Abundant stars, common habitable planets, very slow tech. Always the Drengin and the Yor (I haven't played a game with Korath in ToA yet).