This is good advice.

A lot of those scientific programmers have at least a MS in amath or an engineering discipline. PhDs are extremely common for the people writing adaptive meshers for fluids. Plus they are pretty good programmers.

Experience building websites and an undergrad CS degree does not get you that job. In fact, an undergrad CS is (imo) a waste of time. From CS, all you need is programming skills / data structures. You need a graduate level understanding of PDEs and linear algebra to do most fluid work.