I think the implication is that an atheist would go through secular channels, such as informal counseling, organizations like AA and Al-Anon (just for examples), and if the need is severe, clinical therapy. Or, depending on the people the atheist knows, they might even point the needy person towards pastoral counselors, gurus or other combined spiritual and mental-health mentors. It all comes down to their individual experience.

(Just for reference, my grandfather is a devout Christian of the pastoral counselor variety, very knowledgeable about Psychology, of course, who has worked his whole life helping people in a secular manner, even though his background is religious. They aren't mutually exclusive.)