Technically, you are demoted as soon as you reach the threshold. Similarly, you SHOULD be promoted as soon as you reach the threshold (eh 1100) but sometimes it happens earlier. You might get to play on arena 4 with 1050 trophies simply because there is no one currently looking for a fight from arena 3 that has as much trophies as you, and would be a suitable match, and yet, there is someone from arena 4 (say 1101 trophies) looking for a fight, that the system says is the best match for you. That's why when you start the game you see "Visitor You" sometimes.
TLDR: If the system finds you a player to fight, that has few trophies more, and is one arena above, you'll fight each other instead of waiting 20s or 20m for player your arena and your trophies to come.
Source: Personal experience.