This is because your interpretation of 'day' is of being a subcomponent of a 24 hour period (which probably also includes 'evening' and 'night').

The definition Amazon and every other company offering 'next day delivery' is that 'next day' means 'the next day'. As in the day after you buy the thing. It's a much more reasonable interpretation of the term because it's not open to colloquial misunderstandings (in your interpretation there could be day, evening, dusk, night, etc.). Is 5pm day? Is 6pm day?