It seems to me the reason is that he has the custom value of the unit, which is basically just a number, set as a RANDOM between 1 and 2 for the first movement triggers, if the unit's custom value = 1 it sends the unit one way, if it's 2 the unit goes the other way.
To edit this so the unit only goes down 1 path you need to remove the movement triggers and redo them. I suggest starting from scratch because jumping into a TD with a bunch of Variables in it already is hard to comprehend because whoever made them does it in his/her own way. He set all the movement triggers using variables instead of regions, which is good, but not for a beginner.
If you want an easier way to start off your TD making experience, download the version I edited and take a look at Red's movement triggers, they are honestly less efficient than using variables, but they are much easier to make and copy/paste.
Map
If that was not the problem you were speaking of, there is also another problem. I found out while experimenting that if you maze and the units touch other points on the way to their first point, they will follow that trigger instead of the one they were currently following.
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Events
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A unit Enters Red Spawn <gen>
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Conditions
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Owner of ((Triggering unit) Equal to hostileCreeps (This just means it is owned by Player 12 (Brown)
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Actions
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Unit - Order - (Triggering unit) to Move To (Center of Red Move 1 <gen>)
This, of course, sends the unit to the said area. BUT, if on the way he encounters another region (AKA another way-point), he will instantly drop the other trigger and go to that said region/area instead. So if the trigger is:
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Events
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A unit Enters Red Move 1 <gen>
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Conditions
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Owner of ((Triggering unit) Equal to hostileCreeps
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Actions
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Unit - Order - (Triggering unit) to Move To (Center of Red Move 2 <gen>)
The unit will go to Red Move 2 instead of the original Red Move 1.
To fix that you either need to put in some Boolean Values/Variables, or block the region from the creeps somehow until they enter the first one. If you need some help with that let me know.
I hope that helps you with your problem.