Is it obligatory for a young man to stop tutoring girls at home when he feels an inclination towards them, especially in seclusion, or how can he continue tutoring?

It is not permissible to be alone with a foreign woman (non-mahram), whether for teaching or any other reason. It is also not permissible to teach foreign (non-mahram) girls; teaching should be limited to males only. One must beware of being complacent regarding the temptation of women. Whoever is able to marry, let him do so promptly. Otherwise, let him be patient, remain chaste, fast frequently, guard his hearing and sight, keep company with the righteous, and occupy his time with beneficial deeds.