So I bought a modded Squire 51' yesterday that had Seymour Duncan Rails Strat neck and a stock humbucker bridge. Keep in mind that the rails are apparently humbuckers and the pickup that was originally there was a single coil.  The guitar also has coil splitting that from what I read only affected the stock bridge humbucker and would do nothing to the single coil neck. Well that's not the case with the Seymour Duncan as there is a definite sound change when using the coil split.  That makes me assume that whoever put in the the Seymour Duncan did that on purpose and knew what they were doing.

The problem is that when I put the pickup rotary on the mid position (using both the neck and bridge pickups) there is a significant volume decrease and the tonality is thinned. However, when I play with distortion, there's hardly any sound difference when in the bridge position or the mid position, they just sound like a normal bridge pickup being used. I'm not sure if this normal, because no guitar I had before this made a sound like that in the mid position. Then again, I've never used a brand name pickup, much less mixed pickups.

Can anybody explain this to me?
Sounds like the pickups are out of phase with each other (basically one is wired "backward" compared to the other). In a guitar with 2 pickups it's a simple fix. Just swap the hot and ground connections of one of the pickups.

Since the bridge pup is stock, it's a good bet that the previous owner wired the neck pup backward (though if they were fiddling with the coil split wiring then who knows what all they were messing with).
Invader Jim I contacted a technical specialist at Seymour Duncan and they said something similar. I have idea how wiring works, nor do I know how solder, but they said it's probably that the pickups are out of phase and it be fixed by simply swapping the black and green wire positions.

It confused me too that the coil switch work with the pickup if it's true that they installed the pickup wrong. I guess I'll just go to the guitar store I got it from and ask them to inspect the wiring and tell them about the out of phase pickups.
Fender/Squier pickups are wired out-of-phase with SD pickups. The easiest thing to do is reverse the hot & ground on the Squier pickup, and your sound will come back.
Sadly, there is no standard for wire colors or phase relationships among pickups. 
Dave @ Seymour Duncan