Hrmm. It definitely sounds interesting. Though not sure how I feel about the time skips within a single book, those have a tendency to annoy and confuse me unless it is a time skip between books.
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Well, it looks like the college portion of the story only takes up the first half of Book 1. The main character (Quentin) is already in his Fifth and final Year at the college.
The book (or the first half, anyway) is therefore structured like a series of vignettes. We skip to the important, pivotal points along Quentin's journey from the First through the Fifth Years of his study; each chapter focuses on some important or noteworthy event that happens during this timeline. We also get plenty of overview of what he does and his progress in mastering magic. I find it very easy to follow, since it's very linear (e.g. "Three months later, Quentin was doing X, and had made progress with Y, but then Z happened").
Quentin is a fairly flawed protagonist, so he's rather angsty, especially starting out. The accelerated unfolding of the college experience serves to further underline the ways in which he grows and matures from an angsty teen into a relatively functional young adult. And of course, we have the various friends and acquaintances and faculty who come and go, as well as Quentin's periodic visits back to the outside world.
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In essence, your concerns shouldn't apply here, since the jumps forward are very linear and clearly demarcated. It's not a non-linear affair where we jump from past to future and back again, and nor are we dropped into some future date with zero context. In terms of chronology, the book reads very smoothly.
I'll tag you when I've finished the second half of the book, to relay my impressions on both that half and the book as a whole.