A bug I had noted in Publisher 2007 & 2010 is fixed by this simple change to the page size settings:
After following your steps I see the same problem in Publisher 2010 and Publisher 2007 Service Pack 2 but not in 2003 Service Pack 3. I see the 5 rows of 2 in 2003 as you are expecting in 2010 but not getting.
What type of Avery labels are you printing?
If you have the existing Publication open that was set to Northamerica 2 x 3.5" try changing the page size to the Avery preset by going to the Page Design tab, selecting Size, and clicking on More Preset Page Sizes..., selecting Business Cards, and either Avery A4/A5 or Avery US Letter.
If you are creating a new publication in 2010 but in step 4 choose the Avery preset.
By setting the page size to an Avery 27871 and changing the orientation to portrait, the 10-up printing works as it should.
Trying to set up the page via the blank business cards still doesn't work.
So the question is, what is the Avery template setting inside Publisher 2010 that the blank template isn't.