It shouldn't matter if you play on the website or the app. The trophy is applied to the account, not the device.
That said, it might be possible that the app withdraws you from a tourney after the last game is played by the app user and if you are withdrawn before the last game in the event, you don't place. Not 100% sure why that is done that way.
Read a thread (which can't find now) where was discussed not being awarded live tournament trophies played from Android app. Anyone know if this problem has been fixed?