What I'm trying to do is get a solid understanding of what software, and what forms of playback, and to what devices or software you are using. There are many things involved here, and which ones are being used, depends on how you do things. But I'm still having difficulty understanding what device, what software, and what forms of control you're doing.
Let's avoid restating any more *what* the problem is. I get that. Tracks repeat, and the playing indicator is incorrect. OK, got it.
It sounds to me like you are use JRiver MC to start playback (because in JRemote, there is no play button at the top left, and there is in MC). And you are watching the playback status for the zone on JRemote, and it is not correctly tracking what MC is doing.
Please confirm again you do not have Repeat enabled on both MC and on JRemote.
Also, how does your Plinius Tiki come into play? Does that show up as a zone in MC, and you are playing back to that device, and that's when the problems appear?