Well... seems to me not! This morning I've done 3 misssions in a low populated System for a Faction in war elsewhere and... no influence rises! I'll verify more!
Is every other faction with meaningful influence in conflict in that system?
Note, factions in conflict have their influence locked, and other factions out of conflict can't bleed influence from them.
Elections also count, as do pending wars/elections, as do recovering wars/elections (and the recovering ones are a pain to spot)no factions at all in that System are in war...