Natives tend to use ‘the next day‘ when referring to past actions.
For example: He felt ill on Monday but he decided not to tell his wife until the next day.These are actions set in the past. You can also use ‘the following day‘
Use ‘next day‘ when referring to future actions.
See you next day.
Tell me next day, I don’t have time now.
These refer to future actions. You can also use ‘tomorrow‘