How might data be collected for this target response?I would do observations and encourage the supervisor do this as well, with consideration that there might be bias from the supervisor I would look for another individual for input as well. Staff questionnaire?
Identify several interventions that might help improve response rates. Place them in order with the least-restrictive at the top so that the interventions may be introduced systematically, adding more restrictive / less favorable interventions after the outcomes of less restrictive options have been measured.

Begin by scheduling increased supervision, collecting data on staff response target behaviors (such as accessing data binders and client engagement). After several days, review data to see if desired effect on behavior change is observed. If not, move into performance feedback for staff who have not met target criteria. Once this has been implemented for a few days, use data review on targeted staff behavior, and, if needed, add in an intervention for highlighting staff performance more publicly. This might include a group contingency/summary of performance data. For those not responding well to the interventions so far, consider reduction of task/aversive components while you train up desired skills.