Hi,
I've been having this issue as well and finally resolved it, so I hope that this will work for whoever else has this issue.
In addition to my home screen not rotating properly (until I swiped the screen or opened a folder), I noticed that the rotation on my lock screen was not working properly either; most of the screen would rotate fine based on the orientation, but the menu bar at the top (with the time, battery icon, and other icons) would not rotate along with the screen.
After extensive tinkering (hard restart, reset all settings, restore to factory settings, playing around with any setting that affects the menu bar at the top, etc.), the one setting that fixed it was toggling off "Speak Screen" in General > Accessibility > Speech (this is the function that reads the screen with a two finger swipe from the top bezel). Once I toggled this setting off and performed a hard restart (holding power and home buttons simultaneously until the Apple logo shows up), proper home screen rotation was restored.
Not sure that this will resolve the issue for everyone, but I figure I should share this in the hope that it will help some.
Godspeed.