I am afraid that the Asian house gecko can't be placed in the category
of "self-introduced". Their success here is related to human-assisted
arrival, particularly by ships into northern Australia. Populations have
been shown to radiate from ports.
Further, this species is no longer confined to urban dwellings, it has
spread into bushland (i.e. around Darwin etc) and has the potential to
displace/outcompete native gecko species. A similar situation is
occurring here in Brisbane.
There are also now cases where the Asian house gecko has been recorded
feeding on native skink species.
Best regards, Pete Kyne
Brisbane, Queensland