I've seen the same popup across multiple websites when viewing a site in safari on iphone. For example viewing wunderlist.com and vsco.co yield the same popup when viewed on iphone on safari prompting the user to download the app. Is this something baked into safari or is this a plugin? Maybe they are built from scratch but it seems like several sites are using the same popup....
Yes, there is and it's based on a meta tag.
<meta name="apple-itunes-app" content="app-id=myAppStoreID">
You can also provide other (optional) parameters for example to generate better links for the already installed application (you can link to specific content inside the app):
<meta name="apple-itunes-app" content="app-id=myAppStoreID, affiliate-data=myAffiliateData, app-argument=myURL">
See more information here: https://developer.apple.com/library/ios/documentation/AppleApplications/Reference/SafariWebContent/PromotingAppswithAppBanners/PromotingAppswithAppBanners.html