There're both Appointments+ and BuddyPress plugins active on site. A+ is set to not auto-confirm appointments and to let service providers set their own hours and to confirm their appointments. A service provider should see his/her appointments in BuddyPress profile and be able to confirm them there.
With WPLMS Instructor theme they can see both Appointments tabs in BP profile but "My appointments as a service provider" one is empty. Switching to default (Twenty Seventeen) theme immediately "fixes" that so there's some incompatibility.