Yeah, this is so weird. I have the same problem with the YouTube app on Android too. I believe it used to work by pulling down to refresh. But Google removed that because it's an Apple patented feature apparently. But it seems Google never added in alternative way to refresh the "My subscriptions" list. I found that if I go to "What to watch" and then back to "My subscriptions" it sometimes refreshes if it's been a while. But if I try to refresh it again 10 minutes later it won't. I have to exit the app, long press on the YouTube icon on my desktop, go to App Info and force stop YouTube, then start it back up. Come on Google, that can't be the way it's suppose to work?
Just blows my mind there is no refresh option in YouTube on Android.