Is it normal/ethical for student grades to be assigned according to quotas?
Unfortunately, the universities and colleges are run by managers and not only by academics. In ideal world, all students' work should be marked according to its merit; for example, if all mathematical problems are solved correctly, then the paper deserves 100%. Academics usually understand and share this view (apart of a few strongly believing that "no work ever deserves 100%").
Unfortunately, people who manage universities, are not always guided by common sense or mathematical reasoning. They seem to invent some obscure metrics and force them on the rest of academic staff. Academics do not think it is correct, but they have to play by the rules which are set by non-academics.
Unfortunately, students become a collateral damage in a clash of two cultures: academic and management. If you want to query this, best ask not your professor, but a Dean (anonymously or as a part of larger group). The misguided policies arrive from the very top; your professor has not much power against it.
Yes, this is (unfortunately) fairly normal in the sense that it is done at a number of locations.
The places I've heard it done, the main concern is at a department level, with courses of many sections, in which instructor difficulty has high variability; some instructors are "hard" and others "easy". Admittedly, this causes some initial level of unfairness in the luck of the draw as regards who each student gets for an instructor. The fixed-statistic doctrine forces the harsh instructors to scale up grades to look more like other sections, and so forth (this reduces student complaints to the dean/department). The resulting counter-unfairness is that if lots of legitimately strong students all get in the same section at once, they will be effectively penalized... however this becomes somewhat masked because the grade-data is now mangled, and all you have left are subjective student complaints that are likely ignored. I know that I've had multiple sections of the same course in a semester, taught identically, with wildly varying outcomes (40% passing in one section and 80% in the other).
I think the gold-standard way of handling this would be to have joint tests that are team-graded (i.e., same one or two professors grading each problem and verifying each others' judgement). However, that is logistically expensive and rarely done by tenured academics, I think.
My father had a similar down-grading in a college class, for similar reasons, circa 1966 and he hasn't stopped complaining about it yet.
While it sounds like your professor may have originally been grading too easy, increasing the difficulty of assignments and grading on a curve are different.
If it is on a curve, on the topic of ethics I'd make the following argument against grading on a curve, which may give you some traction if you try to get this policy changed:
Grading on a curve turns grades into a zero sum game, which penalizes group study and makes the class competitive rather than cooperative: the better you do, the worse off I will be. It's now in my best interest not to help you (and to actively harm if I'm so inclined: peer reviews being a prime candidate), because that will maximize my ranking on the grading scale.
This actively harms all student learning, as teaching others is one of the best ways of learning material and this disincentivizes students from helping/teaching one another: Those who would be willing to teach should, if working from their best interests grade-wise, not. Those who need additional help are then less likely to receive it.
One of the articles I most agree with around the web on this topic is Why We Should Stop Grading Students on a Curve which covers this topic with more depth, to include that this idea of life being a zero-sum game is ultimately to the student's detriment.