"Front Page" in Safari does not re-direct

Configuration: Front Page 6.x-1.2
acquia-drupal-1.2.7

Mac OS X 10.4.11
Firefox 3.0.9
Safari Version 4 Public Beta (4528.16)

For the same (Drupal 6) website:
If I log in using Firefox, everything works fine, and I wind up at http://www.example.com/node
which is the proper re-direction for an authenticated user.
If I log in using Safari, I wind up at http://www. example.com/front_page
and I'm not logged in at all. But if I try to log in again, then it works.

BTW, for Win XP-pro, the website works just fine for:
Firefox 3.0.8
Safari Public Beta 4
and IE6

So maybe it's a Safari on OS X glitch.
But it's weird. To summarize: For Safari (public beta 4) on OS X,
I have to log in twice to get re-directed to the right "node".