Read up on replacement effects (rule 614.). The gist of that is what I was trying to convey.

But the creature does not die. That is the crux here. It goes to exile DIRECTLY. The sequence is simply

Token on the battlefield -> token in exile -> token ceases to exist

And again, there is no trigger from Rest in Peace. Because the exile is NOT a triggered ability.

Also the "token" part is nessessary because Rest in Peace otherwise would only affect cards, and then the token would be able to die.

Your reading skills are subpar:

"If a card OR TOKEN would be put into a graveyard from anywhere, exile it instead."

Also, a replacement effect REPLACES the event. So the permanent never even touches the graveyard. Rest in Peace also only has an ETB trigger to clear all graveyards. The rest is not a trigger. Your expected sequence is not how the game works.

614.1. Some continuous effects are replacement effects. Like prevention effects (see rule 615),
replacement effects apply continuously as events happen—they aren’t locked in ahead of time. Such
effects watch for a particular event that would happen AND COMPLETELY OR PARTIALLY REPLACE THAT EVENT with a different event. They act like “shields” around whatever they’re affecting.

614.1a Effects that use the word “instead” are replacement effects. Most replacement effects use the
word “instead” to indicate what events will be replaced with other events.

Read Rest in Peace again. Nothing died in your scenario, nothing was put into your graveyard. The token was EXILED INSTEAD.