Yes it is common, but that doesn't mean it isn't worth clarifying with the university. The way that offer letter it written it could be an offer of 12 monthly checks of $4,170 ($50,000 total) for nine months of work. I could also read the same sentence as saying: The salary for a full year of work is $50k, but we're only hiring you for nine months so we're offering you $37,500 (3/4th of the full annual salary).
I'm in a 9 over 12 position and I've often wondered what would happen to those last summer checks, which in principle are deferred pay from during the 9 months the university pays me, if I left in the middle of the year. Good to know that, based on your partner's experience I should be on the lookout for weirdness and/or try to time my resignation for August when the pay deferral resets.
Some schools (but not mine) will let you opt out of 9 over 12 payments and just be paid a bit more for nine months and nothing over the summer. Mine doesn't. But if you and your spouse are both MMMers it shouldn't be hard to set aside the right proportion of each paycheck to be able to cover expenses and pay for things like the employee portion of the healthcare plan out of pocket over the summer.