Annoying Bone Rotation Glitch? My english is bad. I apologize for my bad english.

I've been watching tutorials and learning on my own too, but I cannot seem to be able to find a solution to this problem in particular, or maybe I simply don't know how to describe it. :(

Context

I am rigging a large dragon model for a game. When it comes to the tail bones, I have 3 bones making his tail and they have the limit rotation constraint, but the bones seem to ignore the constraint.

When I'm testing the Y-axis rotation limit, instead of going up and down, it makes a kind of an "S" shape slide. Funny and weird, because the bone seems to be entirely ignoring the restriction to not rotate over the X-axis.

This animation will clarify what I mean:



Summary: when I test Rotation on Y-Axis on the tail, first up/down, then it goes to right/left. The tail moves in an "S" shape even though the X-axis is limited to 0:0. I honestly don't know much about rotation engines or measures like Euler or quaternion, I haven't messed with that yet.

I attached a .blend file for further comprehension of my issue.

EDIT

Thanks for the elegant edit of this post, forgot to link the .blend file

https://drive.google.com/file/d/14nmny0wEqOcibfAlXmsPhZO7ZNUYfxFa/view
The rig is working OK. If you bring up the transform manipulator and set it to rotate on local access:



You can visually see the orientation of your bones:



The red circle is x-axis etc. Clicking on these sequentially gives the range of movement you stipulate in the constraint. Notice x-axis is on an orientation I assume you would want the tail to move but you've set it to zero. The "s" shape movement you describe happens when you try to force movement in a direction that is choked by the constraint. 

I also noticed that the bone roll doesn't quite agree with the orientation of the tail (all the bones are diagonal to the axis). I hit ctrl-n and chose global +z in edit mode to recalculate the tail bones. This ensured up/down, side-to-side but not twist movement - again assuming this is what you wanted.

ps. Nice model

Edit: I notice TeeTrinker has already answered in the comments as I was typing this LOL.