In my experience, formal assessments are not done with tutoring services, as most tutors will indirectly assess a client's needs based on talking to them (or family if a child), combined with direct observations of deficits and needs. When talking with a client most tutors will want to know specific academic issues, along with any behavioral concerns. For a client diagnosed with ADHD, or general concentration and attending concerns. they will implement a lesson plan that focuses on short durations of new material, with an emphasis on retaining the information.
In regards to formal assessments, they are typical reserved for other services, such as ABA services. Although this answer will vary by company and funding source, they often consist of a combination of direct observations, informal interviews, and administered formal assessments, such as an ABAS-3, WISC-IV, ABLLS-R, VB MAPP, or AFLS. Once a deficit is indicated, tutoring is sometimes recommended to help with academic deficits associated with the formal diagnosis.