Probably the best way to be aware of responses to your threads in the AC app is to first Favorite the thread by tapping the bookmark icon at the upper right. Then go to the Forums section, tap the dropdown menu at the top, and select Favorite Threads, where you'll see that list. Any thread with a new response that you haven't read will be bolded.
The other thing to do is on the main AC Forums website on your computer. Click on the Settings dropdown menu just to the right of your username and avatar, click on General Settings, then Default Thread Subscription Mode. Change it to "Instantly using Email, Push."