The thing is, this is just how Diablo III has worked since Adventure Mode was introduced. It’s been so long since I played Campaign Mode that it took me a second to remember that the check points would actually start you where you left off. Diablo II is the same way, when you exit the game, you re-start in town, and all the areas are re-populated and all maps re-randomized in the new game (single player saves map layout though).
So I think most guides (for better or worse) are assuming familiarity with Diablo III Adventure Mode, which is needed for the event. So if you’re playing in adventure mode, no “world” progress is ever saved between games, only character progression, items, etc. So leaving in the middle of an area always puts you back in a starting town the next time you login. So having the guide explicitly state this may have been seen as overkill.
In the case of the Tristram event, if you just want to experience all the levels, and don’t care about getting 100% of the achievements, choose your fastest/best character, and just blow through them. If you want all the achievements, you’re going to have to play through the levels multiple times anyway. The good news is the achievements are remembered, even over multiple years. I think it actually took me 2 or 3 Tristram events to get all the unique monsters killed for “Protector of Tristram” since it’s RNG on which monsters spawn, having killed them in a previous run doesn’t prevent them from spawning again (instead of the monster you actually need to kill to finish the achievements) and I had limited playtime/interest to go through it all over and over.
As has been said, if you want certain achievements, you have to start with a new character (although I’ve killed monsters on the way so had more than 0 XP before starting the event before and still got the achievement) and complete all 16 levels at once.
Good luck and happy hunting!