No, the personal tutor role does not require such training. Instead, we train personal tutors to refer students effectively to teams within Student Support and Wellbeing Services. These teams have staff specifically trained in mental health support and other welfare support areas. We expect your personal tutor to be able to direct you to these teams when required and crucially, be available to discuss how any difficulties might impact your studies.
While personal tutors are not required to have professional qualifications in supporting mental health, they (like all staff) are invited to attend various information courses. See How is King's raising staff awareness of mental health?