There's obviously some confusion in your description.
"...runner steps on the plate ump signals safe..."
If the runner really stepped on the plate, the runner is safe. Nothing after that point can change the fact- no tag, or appeal, or complaining or anything else.
Now, if the catcher missed the tag AND the runner missed the plate, here's what should happen:
- The umpire should NOT call time! There is still a continuation of the play going on. The runner can still come back and touch the plate to correct the miss. The defense can still tag the runner before he scrambles back, or make a live ball appeal of the missed base.
- Once the tag and base is missed, the umpire should pause to see if either of the above things might happen. If neither is happening, then signal safe. Just like on any other base, when the base is passed it is assumed to have been touched until appealed otherwise. The "safe" signal indicates that the initial tag attempt failed.
- Keep the ball live at least until the runner enters the dugout/dead-ball area. At that point, the runner loses the right to come back and re-touch home. Up until that point, you still might have the runner coming back to re-touch, the defense trying to tag him before he does or the defense making a live-ball appeal of the miss.
- Once the runner leaves the field, the defense can still execute an appeal up until the next pitch is thrown. If they do, the runner is out and the run doesn't count. If they don't, the runner isn't out and run counts.