I’m not totally sure when to use a reflexive “metre” as opposed to “commencer.” Is it a tone thing, or is there a strict grammatical rule for this?
No, I don’t think this is a grammatical question. Se mettre à (deux t!) et commencer à are practically synonyms… Maybe it is a question of style. But it is different when there is no infinitive following.
You can say “il a commencé à parler” et “il s’est mis à parler”. But in the case of “La Révolution française commença en 1789”, you can’t use “se mettre”.
it’s just as in English, you have different words to mean “begin”, “start”, … which are used in slightly different contexts, sometimes interchangeably, sometimes not
Remember that “mettre” by itself means “put”
“Se mettre à faire quelque chose” would literally be “put oneself to do something”, “set oneself to do something”, “set out to do something”
Think “undertake” for an English equivalent, not too far in meaning and use