Well clearly sync only makes the beats the same! Quantise is what makes the beats START at the same time. Not all software has that feature on iDevices or Android and if they do, you have to make sure it’s turned on.
It is curious that you can do it with two identical tracks and not with two different tracks. I do think that would be a beatgridding problem.
Obviously starting a track in time is trickier on a phone/tablet than it is with hard wired play buttons on controllers/TTs.
Finally I am assuming you let the software analyse all your tracks before attempting sync? And then you may have to look at the beatgrid to see if the software did it right (anything over 70% correct is already awesome imho, but still leaves 3 out of 10 wrong) and correct it if necessary. Also this software isn’t always the best with flexible beatgrids (i.e. software that isn’t done with a nice tight computer-generated beat).
To get back to the earlier point. If you use the same track, it really doesn’t matter where the software set the beat markers. Since they are in the exact same spot, the tracks will play in sync. Even if the beat marker is half a beat off. If another track is on beat though, then they will play, well, half a beat apart.
I know it works, I used DJay, DJ Player and Cross on my iPad and iPhone and it works as advertised.