Making my fps a multiplayer

So, I have been partially following (Using some of the code and just the setup of things) the first section of the FPS tutorial (Here) except I'm using my own models and changing things around to what I want. Now, I'd really like to convert this into a multiplayer game. I tried doing the first part of this tutorial, (Here) and it works, partially. But on either side of the server, when one player moves, it moves itself and the other instance of the player/First Person Controller.

So basically if one player moves, the other player also does the same movement, but only on that computer. I'm lost as to what I should do. If anyone would be kind enough to possibly walk me through some steps toward making this work, that would be awesome.