A good friend of mine is working as a Solution Analyst in one of McK offices.
From his experience, I can tell you that this role is a combination of back office and consulting experience with McKinsey. These people spend part of their time in the office and another part they are assigned to the project teams (sometimes multiple project teams at the moment). They typically do the big data analysis of the huge client data bases to generate valuable insights for the engagement teams.
Depending on the assignment their workload might differ significantly: from 8am-6 or 7pm in case of back office work till "normal consulting working hours" if they are assigned to one or more projects. The last may also include business trips and customer exposure. Therefore, your typical day spent in office or at the client site depends on your current assignment.
I hope this clarifies your question.