MP4 video rendering differently on different browsers and different machines
Unfortunately you are not going to be able to accomplish your goal.  Two major factors impact this.  First, color processing on different systems is going to differ.  This will result in slight differences in the colors that are displayed because many video players apply "enhancements" to video and what you actually see when viewing the video in a browser is an embedded player that is installed on the local machine.  

Second, different software is also going to use different implementations of a decoder which may result in slight differences in color based on optimizations and rounding error based on how they do their calculations to get the video out.  It's just a side effect of the way the players operate, there isn't a problem with your source (as the data in the file can't change from one player to another.)