I got this strange thin with FB all the time.. I dont know if its FB itself they way its made.. but the thing is like this

I got Meenger FB installed on my phone...sometimes push notification when people talk chat with me are entering bu sometimes people are chatting and no sound or push... mostly I`m on my phone AND on the PC browser online chatting..
Should that be the problem that I have on the PC and phone chat window open ? Which one is priority first?
Cause when I have a window of chat on my PC open and suddenly open on my iphone the messenger app and go chat with that person itself..the chat window on my PC closes...

Any one could tell me ? should I go offline on my PC and only online on my phone ?