This is a bit confusing and is not well explained in the Help file.
If you use the Articles panel when creating an Accessible PDF (Tagged PDF must be turned on), it's not controlling what's seen on-screen. It's changing the Tagging order (the order of tags which you can view in the Tags panel in Acrobat Pro. Make sure you go to the Articles panel menu and check Use for Reading Order in Tagged PDF.
The only source I've found which explains this well is Chad Chelius' Lynda.com video "Creating Accessible PDFs":
In particular, in section 3, look at the video on Controlling Tag Order.
You can get a free week when you subscribe to www.lynda.com.