This comes up quite a bit here actually. Basically, Ai ExtendScript is single threaded so when you initiate an action from a script (first thread) and that action tries to run another script (second thread) Ai is waiting for the first thread to end before it can move on to the second.
You could try calling the second script from within the first script like below or skip the use of an action and write those steps in the script (if doable).
// do you stuff from script one
var doc = app.activeDocument;
// call your action (without the other script call)
app.doScript("hey", "example");
// run your second script from here instead of the action
var s = new File(Folder.desktop + "/example.jsx");
$.evalFile(s);