First you need to understand that there are a couple of ways that Closed Captioning can be added to a video. If you are looking at iOS specifically, then the video must conform to the CEA-608 encoding standard, and needs to be either a HTTP Live Stream (HLS) or MP4 video. Other video formats WON’T work on iOS as an embedded video if you need CC playback.
If the video meets one of those to standards, then it’s about the playback setting that are set for the HTML5 web page.
If you are looking to embed a YouTube video on your page. You need to verify that the video has an existing Closed Caption track (not one of the on the fly automatically translated ones).
Below is an example of a web page that should play back a movie trailer for “The Martian” that has had a Closed Caption track created for it.
I have verified this page works on my desktop Mac with Safari and Chrome, a Windows 7 laptop with Chrome, an iPhone 6 with iOS 9.2, and an iPad Air with iOS 8.4.1.
<!DOCTYPE html>
<html lang="en">
<head>
</head>
<body>
<div style="overflow:hidden;height:270px;width:400px;">
<div id="youtube_canvas" style="height:270px;width:400px;">
<iframe style="height:270px;width:400px;border:0;" frameborder="0" src="https://www.youtube.com/embed/aIL01wrwq6w?hl=en&autoplay=1&cc_load_policy=1&loop=0&fs=1&showinfo=0"></iframe>
</div>
<style>#youtube_canvas img{max-width:none!important;background:none!important}</style>
</div>
</body>
</html>
The key code bit for YouTube videos is the &cc_load_policy=1
you already have found.
But if the video you have linked to does not meet the original video specs, then you will never see CC text in iOS. The native YouTube player will play back videos not in the CAE-608 standard, but iOS through a web player will not.
If you need to do this for your own videos, then you need to make sure your encode creates a CEA-608 embedded CC track.
I hope this helps.