How many visitors did Organia get? Not many, by the looks of it.
The very fact (false, but Kor doesn't know that) that there was a Vulcan merchant there would appear to establish the "visitors" thing, a means for the Vulcan to move his merchandise etc. If Kor wanted to deport the Vulcan, he could certainly tell the man to contact his organization and get the hell out of Dodge. Apparently, for some reason, it wouldn't be a factor that Vulcans were UFP members and far from neutral in the conflict - so letting a Vulcan transport pick up the businessman should be okay, too.
I think the big question here is, why didn't Kor's interrogation technique work? Why did he trust that Spock was as bona fide as bona fide gets when in fact his technique was so thoroughly faulty? Had it perhaps worked on Vulcanoids (say, Romulans) before? And if so, why was Spock able to thwart it?
I could well buy Kor not really minding the two suspect civilians. The trouble they caused by blowing up the munitions dump wasn't that big a deal, and arresting the duo afterwards should have been the end of it. We never learned if the Klingons wanted to eradicate the Federation once and for all, or merely to gain a few more systems - but the latter goal would be better reached if Kor didn't burn too many bridges, whereas only the former would call for ruthless crushing of all resistance. And that only if Organia really mattered; a true Armageddon conquest campaign would involve moving on soon thereafter, and the Empire should not really be interested in the strength of its grip on the backward little planet in that scenario, unless Organia had some inherent value we weren't told of in addition to being a strategic stepping stone.