You guys are missing the point. The biggest issue here isn't what it *should* do, it's that it is inconsistent. Sometimes it takes me home, sometimes it takes me back within the app. It should only do one of those every time. Not randomly switch between them.
And really taking me back to my previous app makes more sense than going home, which is what it does most of the time. It rarely goes back within the app like couch mentioned. If I go from one app directly to the other app and hit back, why the heck should it take me to the home screen where I never even was? I never used the home screen to go to another app, so why take me to it? At no point does that make sense. What does make sense is it taking me back to where I was.
If I'm in Chrome and switch to messaging and *immediately* hit the BACK button, it should go to where I just was, which was the previous app. Going back within the app wasn't the last thing I did, so the back button did something I didn't just do, thus by definition not a back button. It would at that point only be an app-specific back button. But in reality it isn't that either.
If I am in messaging and hit a link that takes me to chrome and immediately hit the back button, it *actually* takes me back to where I was! Hey that's awesome, the back button actually does what it sounds like it does, takes you back to where you were. The problem is that this only happens with links and isn't 100% consistent and will sometimes take me back within the app.
Yes, it bothers me that the back button doesn't always do what it sounds like it will do. But ultimately the issue is its consistency. If it is consistent, it at least makes it easier to get used to it working the wrong way.
Sure the back button can be more consistent in general. What it shouldn't do is switch between apps.
Again, why are you not using the app switcher? The button that actually does what you're asking (albeit requiring two steps as any app switcher does).
When I switch between apps, hitting the back button takes me back within the app. I ask again how would you go back within the app then after a switch in your scenario.
You're taking the back button too literally. And at the same time ignoring the button that would do what you want.
Sorry the back button doesn't work for you but thankfully its not the way you want it to be. It'd be frustrating and redundant.
EDIT:
If I am in messaging and hit a link that takes me to chrome and immediately hit the back button, it *actually* takes me back to where I was! Hey that's awesome, the back button actually does what it sounds like it does, takes you back to where you were. The problem is that this only happens with links and isn't 100% consistent and will sometimes take me back within the app.
And I want to address this specifically.
What you're describing is intentional. You are not actually switching to a different app in your example. Tapatalk is not alone in doing what you're describing. Hangouts (and I believe Whatsapp) does this also. This is by design.
You are launching the browser from said app (in your example, Tapatalk), so you're technically still reading the link via the original app. It's just using Chrome to do it.
The example you keep giving, however (going from Chrome, hitting the App Switcher, then going to Tapatalk) is different. Here, you've actually used the App Switcher to get to a different app. The back button should have no relation to the previous app that you switched away from anymore (again, that's why the app switcher button is there in the first place -- to switch apps. That's the button you'd use to switch back to Chrome if you so desire).
Once you've made that conscious decision and action to switch apps (using the app switcher) it makes perfect sense for the OS to believe you want to be in the new app and want to be using the new app. Thus, the back button acts as a back button
within the app or until it reaches the furthest "back" it can go within that app, in which case, it'll take you back to the home screen.
This makes perfect sense.
Whereas, if you click a link from Tapatalk or Hangouts, you're just visiting said link (because it's a link. That's what you do). The OS still considers you tied to the app from where the link came from. This, also, makes sense. Thusly, the back button in this case does precisely what it's supposed to do, take you back "within" that app (Tapatalk/Hangouts). Remember, you're still tied to the original app. The back button never acts as an app switcher. Technically, you haven't switched apps. You're just reading a link.
I hope that made sense. The back button is actually doing exactly what it's supposed to be doing in the examples you keep giving. Try it elsewhere; it's not only Tapatalk.
It's not a coincidence this only happens with links. It's not like it's a conspiracy where once you hit a link, then the back button does what you're wishing it'll do. It's by design.