Teaching assistants (TAs) that lead reformed recitations and labs must understand and buy into the design of the course and the research-based instructional strategies that the course requires in order to create high-fidelity implementations. We present a model that outlines possible influences on TAs' buy-in and their in-class actions coupled with a method, using a Real-time Instructor Observation Tool-based [E.?A. West et al. Phys. Rev. ST Phys. Educ. Res. 9, 010109 (2013)] exercise, to measure the effect of these influences that is not only quicker than interviews but also allows one to quantify these effects. We use this method to measure the influences on six graduate TAs teaching algebra-based introductory mechanics and electricity and magnetism recitations and labs ("mini studios") at the University of Central Florida. The results from the exercise are confirmed by interview responses from the TAs. We find a relatively high degree of buy-in to the design of the course, yet this is not reflected in the TAs' actions. The TAs' actions appear to be most influenced by student responses and expectations which do not align with the design of the course. Our study examines the effect of three influences shown in our model, and we argue that our method could be easily adapted to examine additional influences.