I am wondering if it's possible to do large time skips, large time rewinds into the past between chapters without any explicit indication and make the readers somehow figure it out for themselves. Is this totally ok and has it been done before and how do you make sure the story is correctly interpreted, or it doesn't matter if the readers completely and perfectly understand your story?
One example of this which works incredibly well in my opinion is Cecilia Dart-Thornton's Bitterbynde Triology - the way in which she treats time-based layering and latticing and links multiple worlds and dimensions is masterful.
As you read through the books, layer upon layer of back story is revealed, rather like unpeeling an onion.
As a writer, if you are clear on what the chronological timeline is, and are starting 'in media res', and have made it clear (or clear enough) to the reader where they are, surely then you are simply engaging in building a game for the reader to play - if the 'rules' of the game are clear, and they have enough to inform and entertain them on their journey through the story as readers, you'll have done a good job. If you take it a step further and make the game beautiful, you'll have engaged them artistically as well as intellectually. Whatever story you're telling, you need to decide whether you're plotting a guided tour, a mystery tour, or a treasure hunt for them - the story will be the same, but the narrative treatment very different.
Try applying the technique(s) you want to use to the retelling of a traditional story and see how it works.