As far as I can tell, the only 100% accurate tracking is occurring with Facebook Mobile App Install ads since they have an integrated solution with the App store. But there are many 3rd parties that claim to do it, but my understanding is that it's a "correlative" confirmation, not a true confirmation. Which is the best?
It's a difficult problem to solve for all of your advertising outside of Facebook. Yes the other vendors use correlation to determine with a high probability that a particular user that installed your app is the one that click through a few seconds earlier. Most of the good ones are fairly accurate: above 90%. The one I found that handles the most advertisers is http://mobileapptracking.com/ by Tune. Hope this helps.