While this is a convenient shorthand, it should be noted that cantrips are still spells. This matters in many cases where some sort of ability or feature affects your spells, which includes cantrips. This is why some features specifically call out casting a spell "of 1st level or higher" or "using a spell slot", neither of which would include cantrips.
Not so, reaction spells are generally cast not on your own turn, so you can (almost) always cast a leveled spell as a reaction. You're getting turns and rounds mixed up.
EDIT: Whoops, didn't fully read what you wrote, you are actually correct here. This is one of the rare cases of casting a spell as a reaction on your own turn.