Stats on the stats page are categorized by card, since the "Hands Completed" section is card-specific. They can also be filtered by time period. You can select the card and time period at the top of the page.
If it looks like your recently played games are not reflected on your stats page, make sure you've selected the correct card and that the time period is set to "All time".
Note that ratings are calculated periodically during the day and not immediately after each game.