That specific rule (reaction spells are cast in response to a specific trigger which can occur on your turn or someone else's) doesn't state that it trumps the other specific rule (when you cast a bonus action spell, the only other spells you can cast on your turn are cantrips).
So which one is more specific? Let's look at what they let you do:
Reaction spells can specifically be cast on your turn your someone else's turn. (There is no such thing as "not part of a turn". Everything happens on someone's turn.)
Bonus action spells specifically limit you to cantrips on your turn.
The bonus action spell rule is actually more specific, so it trumps the reaction spell rule. You can only cast a reaction spell after casting a bonus action spell if the reaction spell is a cantrip.
Actually, the most specific rules in place are the individually specific triggers and effects for every reaction.
Generally, if you cast a bonus action spell, you can only cast a 1-action cantrip during the rest of your turn. This applies every time you cast a bonus action spell. Reactions, however, only occur when their trigger occurs, and only do what they say they do - no more or less. So, if someone (or something) else triggers a reaction, and you chose to use your reaction, you can do that reaction then before anything else happens. If that reaction is a spell, then the trigger must happen and then you can only use that spell for your reaction. This is far more specific than the general bonus action spellcasting rule because it only obtains in very specific circumstances (the trigger) and only has very specific results (whatever the reaction ability allows). In other words, the more general rule is what you normally do on your turn, including restrictions on bonus action spellcasting. The specific rule is the specific text for each reaction - their trigger(s) and allowed special actions.
Reactions are, by nature of their narrow rules, more specific than the general case of bonus action spellcasting.
Now, you can disagree with that, but then you're faced with a situation where a reaction's trigger can occur but the reaction cannot happen. IE, I can trigger my use of counterspell, use my reaction to counterspell, but be prevented from counterspelling. I honestly can't think of another situation where that can occur. I'm sure someone can help me on that,, though.
