The concept of "outside-in" within the context of the article involves looking at how your environment is affecting your mental health. In other words, how the world around you (people you see, people you talk to...) is causing or worsening the depressive feelings and work on changing those things first.
There are a lot of articles online concerning Behavioural Activation, which is the form of behaviour therapy developed by Skinner discussed in the article you linked.
One meta-analysis (Cuijpers et al. 2007) found it very effective, and there are a couple of books on the subject.
- Behavioral Activation for Depression: A Clinician's Guide by Christopher R. Martell, Ruth Herman-Dunn, and Sona Dimidjian (2010)
- Behavioral Activation: Distinctive Features by Andrew M. Busch, Jonathan W. Kanter, and Laura C. Rusch (2009)
Cuijpers, P., Van Straten, A., & Warmerdam, L. (2007). Behavioral activation treatments of depression: A meta-analysis. Clinical psychology review, 27(3), 318-326. doi: 10.1016/j.cpr.2006.11.001