Threefold repetition

https://en.wikipedia.org/wiki/Threefold_repetition
It's a draw on white's 9th move because that is the 3rd time that position has appeared. Compare it to white's first and 5th moves.
On chess.com after a position appears for the 3rd time, AFAIK you then have to click the draw button. At that point it's not a draw offer, the site will automatically end the game as a draw.
On some websites once a position happens a 3rd time, you don't have to do anything, it's automatically drawn.
Just making sure I'm thinking correctly...
If the a king is forced back and forth between two areas and in one of them he has two choices...it will be considered a forced draw due to repetition because regardless of the order, the same position will have eventually happened three times? Correct? So, if the checked player were to keep mixing it up, when would an official call be made?