Your quoted info is right. Most high school have first mid-term exam around May 20th.
The problem is magazine system. As you think, most magazine's release date of issue 7 (July issue) is some day of June, because no one buy July issue in August.
But some magazine have more wider shift from titled date. JMPA (Japan magazine publisher associates:Magazine Publisher Associates, which most Japanese magazine joinmagazines are members of) has the less than 40 day guideline for monthly magazine. Publisher (and book store) can sell magazine 40 days before fromthe titled release date oror month. (Weekly magazine have 15 days guideline.)
If the titled date is July 1st, publisher can sell the magazine after mid mayMay. ofOf course, this is most extreme case., but it's possible that people can read issue 7 in May.
To evidence, Youyou can find example from Amazon.co.jp magazine corner. For example, this magazine is July issue (07月号) but amazon startAmazon starts sending that magazine mid mayMay (2014/5/17). (Yes amazon startAmazon starts earlier than 40 days rule, and some book storestores are angry about this, but amazon sayAmazon says customer will receive the magazine after the date.).
I think fashion magazine has earlier selling start date. ForUsing the above example that, the magazine featuredfeatures topic on how to select swim ware thatswimwear, which most people preparedprepares before summer but useuses it in summer, this. The date rule fits the use case.
weekly shonen jumpWeekly Shounen Jump is officially release aton Monday, but some store selling it from Saturday.