iPhone Videos app only offer a single subtitle track
It seems like, as far as I can tell, that the Videos app on iOS only support one subtitle per language. 

I had two English subtitles that both showed up on my Apple TV (as "English") but only one of them in the Videos app. My workaround was to change the language of one of these subtitles to something other than English using Subler (I chose "Unknown"). Then they both showed up i the Videos app as different subtitles.