I believe they mostly recruit using agencies for this position. Most of the people I know that work at the TSR started from a recruiting agency.
I was contacted by a recruiting agency about an opportunity at Raymond James, however, they only had 1 opening despite having a mass hiring a couple weeks prior.
I had a screen interview and then an in-person interview with both managers of the IT dept.
It was a very formal interview with typical HR and a handful of help desk questions. I felt like despite that I did well in the interview, they tend to recruit a certain 'look' that fits in with the company culture.
Not sure if this was my case or if I was competing against some good candidates.