It just adds a number of liked to the thread or post. you can see thread likes from the forum page and post likes while viewing the thread. its the little box right next to the like button.
I use taptalk and i usto get notification when someone would quote me or comment on my post. Now i have to subscribe to stuff even if i started it i dont get any notification
Can you go into the tapatalk forum settings and select push settings. make sure its enabled. I double checked the API key we use with tapatalk to enable push notifications and it looks fine.