Maybe my memory is faulty but it seems like a lot of teams win the cup the year after they win the presidents trophy. I’m too lazy to look into it
At a quick glance, it's happened 17 times since 1967, but 3 of the previous 5 champions had won the President's Trophy the year before (Colorado - PC 20-21, Cup 21-22; Tampa - PC 18-19, Cup 19-20; Washington - PC 16-17, Cup 17-18)
For comparison, we've had 19 teams win the Cup and PC the same time since 1967, but the last three times that has happened were in 2012-13, 2007-08, and 2001-02, which makes it seem a lot less common, despite having actually happened more in the expansion era.