I recently joined a club that was just promoted to Sleuth division. Why, then, does a higher division..

That is what the team has earned from previous leagues. It shows the number of the highest division they achieved. So your team has reached Private Eye 4 times in the past. It should also show 1 under Rookie which is their standing last week. For example, my team has 14 Sherlocks, 3 Aces, and 1 Rookie at the moment. We are currently Sleuths and intend to promote this week. So next week, it should show 14 Sherlocks, 3 Aces, and 1 Sleuth.