How do I keep my tenure track job search confidential? I work as a research scientist for a tech company. I publish frequently in top venues in my area and, at the same time, I've been adjuncting at well-known universities to teach classes.

I don't feel I've ever left academia, as I keep collaborating and publishing with people from academic institutions, but I want to apply to a few (e.g., 10) tenure track positions in computer science, for a number of reasons that are not relevant to this question.

How do I ensure that my search/applications stay private? 

My manager is well connected with the academic world (despite not being a researcher), and I do not want them to know that I applied and where I applied. Note that I do not need a recommendation letter from them, as I have multiple well-known researchers (faculty members in different universities) who will write one for me.
You should tell your references that you would like to keep your application confidential. The problem is that while the job search process is nominally confidential, leaks happen all over the place. For example, people call colleagues asking for informal assessments of applicants. They may not say the person is applying, but when you get a phone call like that, it is pretty obvious. Another example is that sometimes applicants give job talks during a normally scheduled departmental seminar. These are often "advertised" on the web. Again, even if it doesn't say job talk, it can be pretty obvious. At some point you are going to visit the school (if you make it that far) and meet tons of people. Asking/expecting the search committee to keep things quiet is one thing, expecting the entire faculty is another, expecting grad students and post docs is another.