Simply put, if I'm not mistaken, the mission to intercept the spies with the map is absolutely identical in these three cases (0 fragments, Tear found, in the process of searching for fragments). I haven't checked, but I assume that the penalty for failing the mission is also identical. That's what interests me – what could be the reason for the mission to fail if the spies are late and the Tear has already been found.
The fact that they appear and interfere is understandable. What's surprising is the existence of this mission.
As an option, for example, the spies might have their own piece of the map without which the Tear cannot be found.