Contacting a Professor for a PhD in the US (Engineering)
"Talk to the professor first" is the norm in most of the rest of the world, but in many graduate programs in STEM in the US admissions decisions are made by a graduate admissions committee and students are matched to research supervisors (and funding sources) after they've been admitted to the program.  

It's quite common to have some specialized source of funding (e.g. teaching assistantships or fellowships) for first-year students to support them until they have matched with an advisor who can fund them through a research grant.  

One reason for this is that many Ph.D. programs in the US have substantial course requirements, while in other systems it's more common for the graduate coursework to be completed in an MS degree and the Ph.D. degree only encompasses the dissertation research.  

An important advantage of this approach is that it allows the faculty in the department to compare applicants and pick the best overall group of applicants while maintaining an appropriate balance between subfields in the department.

There's nothing particularly wrong with sending an introductory email to a professor and expressing interest in working with that professor, but don't assume that the professor has the power to admit you to the program.  A response of "Get admitted first, then we'll talk" means exactly that- the professor can't make any promises to you until you've been admitted.   Even then, the professor might want to see how you do in course work before agreeing to be your advisor.