The compression plug serves two purposes. First, the plug and top cap is used to preload the stem on the steerer tube before the stem is tighten. Once the stem is tightened, the pre-load function is done and no longer needed. So, for instance, you should be able to remove the top cap without affecting how the stem/steerer tube/head tube connection. Second, the compression plug supports the inside of the steerer tube against the outside pressure of the stem.
In your case, once you've tightened the stem to spec, I'd loosen both the top cap and plug, tighten the plug to spec, and replace the top cap without tightening it to the point that it pulls the plug out.