"Might have" is correct. When spoken aloud, "Might have" sounds like "might've."
"Might of" is completely incorrect, but, when spoken aloud, also sounds like "might've." There's only the smallest difference, maybe no difference at all. People who didn't pay attention in school and know the language mostly by speaking it may actually believe the phrase is "might of." This can find its way into writing.
I wouldn't necessarily reject the tutor. The mind works in strange ways and I constantly find my fingers typing elementary blunders, when I know better. I can think "they're" and type "their." I can imagine thinking "might have" and typing "might of."
If this is a "community tutor" and not a "professional teacher," you may have found someone who speaks authentic, informal, colloquial English. Depending on your goals, that might be fine; conversational practice, for example. I feel that I am paying a community tutor for the trouble of making and keeping appointments, for a session that is 100% in my target language rather than 50/50, for someone who will be patient with me, and--above all--someone who really will stop and correct every single mistake I make.
I see that italki has nine hundred community tutors in English, but only about half of them claim to speak "advanced" English.