It is my experience that no matter what one does, more budget-friendly chainrings are going to be wonky along with their budget-friendly cog when it comes to variations in chain tension... Though the fixed-gear drivetrain (and secondly the single-speed) is so efficient that any slop should be taken in stride and looked upon with pride.
However, when first implementing a professional-level fixed-gear drivetrain on my own, I still felt a little more variation in tension than I had expected from something so 'finely tuned' and was unnerved. In contemplation on this conundrum, I remembered a piece of advice that was given from an old messenger/mechanic in Minneapolis years ago:
Install the chainring with slight finger-tightness on the bolts and put the drivetrain in maximum tension, to the point of binding (i.e. pull the rear wheel out of the ends as far as possible) and run it through a few cycles: Thus absolutely centering the chainring on the crank arm. Then, after tightening the chainring bolts and properly tensioning your chain, one will find their drivetrain in near-perfect harmony. It works a charm
