From JN
The start and end times are based on the UTC timezone, which does not follow Daylight Savings (springing forward or falling back).
The trophies and avatar rewards were never awarded for the April 5th, 2020 and May 3rd, 2020 Crossover Weeks.
The next Crossover Week is expected to begin in the late afternoon, on May 31, 2020 and run through the following Sunday.