I highly doubt it's a remnant of those languages. First these languages are not related. Their verbal systems are completely different and the trilateral root system is one of the most distinct features of Semitic. Day in Arabic and Hebrew is Yam and Yom, respectively; in Nama--one of the most widely spoken "click" languages-- it's tses. The first two suggest a common ancestor the third, a separate one.
It is thought that the Khoi-san* languages have always been restricted to South and East Africa, even before the Bantu migration. It can be noted that none of the Niger-Congo languages surrounding the Afro-Asiatic branch have click consonants even though many Niger-Congo languages absorbed some click consonants when they came in contact with Khoi-san languages.
And as many have pointed out the tsk sound is used in many other languages even English, which is extremely distant. I agree it's probably just a natural utterance, meaning it's an innate behavior and is easily understood, much like glaring or smiling.
*Many click languages are not considered a part of Khoi-san but have a common home land in southern Africa. It should also be noted that many Bantu(Niger-Congo) languages have click consonants but these are borrowed from those with a common homeland in Southern Africa.
Also, the two surviving northern Khoisan languages are in Tanzania, which means we don't have good evidence how far north the Khoisan family once extended, and clicks don't exist in the eastern Nilo-Saharan languages either.