Is it common for students to complain directly to deans, or for deans to review faculty's message to students?
As a tenure-track person who presumably has the goal of making tenure, you must fall in line with what your dean has prescribed as behavior commensurate with one of their department instructors. If you feel the student has violated some part of the institution's enrollment agreement or your syllabus, these violations should be enumerated for your dean. However, if the dean is talking about tone and messaging, then this is likely an issue of your dean feeling like one of their tenure-track folks are not falling in line with what is expected of a tenured professor at your institution. 

This question--and any answer, frankly--is very specific to your institution and your dean's management style, unfortunately. At the end of the day, if you want to make tenure, you need to consider that your dean will be a powerful voice during tenure review. Even if you don't intend to speak to your students in the way that you feel runs counter to your personal understanding of best practices, I think anyone else would recommend that a tenure-track person ought to focus on behavior and strategies that would more likely result in a positive tenure review.

That means, unfortunately, that you must start sanding down parts of your puzzle pieces so that they're fit with the existing puzzle.