Does "influx" require that whatever is coming in have come from somewhere else?
Solution 1:
The Merriam-Webster page that you link includes a list of synonyms that includes inflow. That is an extremely close synonym, flow being the English verb of choice for translating the Latin fluere, which you will find lurking in the etymology there. The abstract nouns influx and inflow are merely nominalizations of the verbs influere and flow in. The key point here is that these are both verbs of motion, the in being the destination or direction of that motion. So we are talking about a flow of something to the inside of some space, and yes it follows that this motion must be from outside that space.