When in doubt...google Samurai Jack wiki.
Here's what I found in the Aku section:
Hungry for more power, Aku established the Earth as a space-faring world, opening his ports to surrounding worlds in order to plunder and conquer worlds beyond as well. The influx of aliens, ranging from enslaved species to rough immigrants, have made the Earth a hodge-podge of a dystopian society primarily run by tyrants and gangs. The few bastions of peace and hope typically remain out of Aku's wide field of vision.
Okay, so yeah. He has expanded his reach off-world.