The colonies had been settled by 2018 and employed the use of slave labor by replicants. That year, a Nexus-6 replicant combat team staged an uprising, prompting the ban of replicants from Earth.
By 2019, humans on Earth were encouraged to emigrate to the colonies; this was promoted aggressively with advertising extolling the adventure and opportunities awaiting them if they left Earth, as well as promises of financial and personal incentives; for example, all colonists were promised a free replicant for their personal use.
Ana Stelline's adoptive parents moved Off-world, leaving her behind due to her "compromised immune system."
The actual conditions on these colonies are never shown in the films, but the setting hints that the situation Off-world is not as rosy as the advertisements claim. The replicants are designed to survive dangerous and harsh labor and environments. Roy was designed specifically for use as a soldier, recalling the battles he fought Off-world, and it appears that all three other of the escaped Replicants had considerable combat training. Zhora was described as having been a member of a kick-murder-squad. Finally, there is the intensity of the marketing campaign itself; although the Los Angeles of 2019 is a miserable dystopia, its population still apparently requires aggressive promotion and considerable financial incentives to leave for these supposed paradises.