I believe the new rank data is available more or less straight away but as @lysnew says:
This can be seen in the following before and after shot:
After winning a game and returning to the home page(without refreshing) my rank has been updated on the left but not on the right.
I would agree with @lysnew that ‘This isn’t a big issue’ except that it may be responsible for confusing the issues around the ranking system by misleading some people as to the effect of any one game on their rank.