to help Bill and Ted pass history if Rufus would only have lived in a Wyld Stallions society if they passed the class.

Because bowling scores are way up and mini golf scores are way down.

We see this throughout the movie. Like where they say they are going to steal his dad's keys afterwards then hide them. They would have had to pass the report, still have the phone booth, get the keys, and return then all without breaking out the historical figures.

So in the Bill and Ted universe just making the assumption that you're going to follow through with your time travel plans makes them happen. Bootstrap paradoxes are common in their world.