1) Set the time of the alarm on your iPhone - do not press the Start button on the phone
2) Open Pillow on the Apple Watch and press "Start"
3) If you need to, select a sleep mode and press "Next" (if you've chosen for the app to remember the mode this step is not necessary)
The sleep tracking should start normally and the next alarm time should be correct. We are already looking to this matter on our side and an update fixing it will be available very soon.