In Puerto Rico when using the "residence" how is "occupied island spaces" interpreted?
It means just a plantation, no colonists are required.
From the rules:

Residence The owner of the occupied residence earns, at game end,
additional victory points for the plantations and quarries he has
placed on his island. For up to nine filled island spaces, he earns 4
VP, for ten filled island spaces, he earns 5 VP, for eleven filled
island spaces, he earns 6 VP, and for all twelve spaces filled, he
earns 7 VP.
Example: at game end, the owner of the occupied residence
has filled 10 of his 12 island spaces with plantations and quarries:
he earns an additional 5 VP.

No requirement for colonists.