When a creature has the poison special ability, an inhaled poison is listed, and none of their attacks list poison as an effect, when must a creature save vs the poison?
Well, it depends on the monster, the answer is probably somewhere in its stat block.
Take the fungal lizardman's inhaled poison - it's listed as an Aura on the fourth line of the statblock. In this case, the standard inhaled poison rules apply, you have to save the second you enter the area (though you can attempt to hold your breath). As opposed to the Tatzlwyrm's inhaled poison, where it's listed as a special breath-type thing that requires an action, in which case you'd save when it breathes it on you.
EDIT: Based on your further comment you mean the Ascomoid. That's pretty straight forward, it says straight out how its spore-poof works and you only have to save against the spores' poison if you fail the nausea save from the spores attack. You'd save immediately and then of course each turn thereafter until you shake it off (2 saves or 6 rounds, whichever comes first).