I like Rude1's approach of addressing the behavior instead of saying "you're being rude." I recall from management courses that one should avoid starting criticism with "You" (You're being rude, You're wrong, etc.). "You" statements tend to trigger a defensive, emotional reaction, so the person is more interested in defending themselves than listening to what you have to say. The most important thing is to state the expected behavior in a calm voice.
Certainly it's fine for the tutor to talk to him about better ways to behave, if she feels comfortable about it. Otherwise, you may need to talk to him yourself or sit in on a session or two.
Could he need a short break partway through the session? is the length of the tutoring time part of the source of frustration? Or the pace? I tend to get more rude and crabby if I am tired or not feeling well, or if my self esteem is low, or I'm feeling defensive.
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Diagnosed Bipolar II in 2012, Autism spectrum disorder (moderate) & ADHD in 2015.