let the watch do his job. I had simmilar problem. Sollution is that you dont have to push any thing to start or stop the segment. It starts and ends automatickly.
This is a very old post, but it looks to me that the GPS track from the watch is not precisely located over the track. It also looks like the segment itself is poorly defined, with jagged edges. If the recorded track and the segment definition do not align then the segment will not be matched from the run.
I don't use Garmin segments, but I use Strava and it is quite common for bad GPS, or a segment defined from bad GPS data, to create mismatch and nothing found for the segment.