Summer premiere? Why?

I believe there are various reasons... the millennium subject was a big part of Arnold's first comeback vehicle following his heart surgery: End Of Days, this movie had a much larger budget than Entrapment and remember that Arnold back in the 90s was able to attract moviegoers when he was involved in action movies: Terminator 2, True Lies, Eraser... so they probably expected EOD to be HUGE (it ultimately wasn't).

Connery was past his prime and Zeta-Jones was basically an unknown VS Arnold who commanded 25 million per film back then.

Also there was a new James Bond movie opening in mid November 1999, The World Is Not Enough, so they probably also wanted to avoid that one.

September-Early November are terrible months for a medium-budget action-heist movie like this one, those months are mostly left for the Halloween/horror movies and Academy Award material.

During the middle of the Summer it would had to compete against The Phantom Menace (at that time the most highly anticipated movie of all time), The Mummy and The Haunting.

(The Sixth Sense was a surprise hit and was not really expected to be the juggernaut it became).

So the best moment to open the movie was before End of Days and The World Is Not Enough, also before the big budget summer blockbusters, aimed at younger viewers, which were more "fun" and filled with CGI.

Also, back then it was very rare to see that a movie opened in every market simultaneously worldwide, the 7 month advanced release would allow the studio to open the movie in most markets before December 31st.

Worldwide releases wouldn't even be something commonplace today if it weren't for movie piracy, which has forced studios in the last 15 years to try to open most of their movies in every market simultaneously.