That is strange, and something that I hadn't noticed before, but I'm getting what you are getting.
I made a new project with 8 facing-pages, put page numbers on the master, added a section start to page 4, which would have moved it to the right in previous versions, but in 8.12, it stays on the left. I did find a workaround, though.
If you drag a new page thumbnail in the page layout pallet to the left of what is now the new section's page 1 (that used to be page 4) and don't let go of the mouse button until you see the icon changed from a page to a right-pointing arrow, it will drop the new page in place of the new page 1, and move the new page 1 over to the right where it belongs. The following pages will change from left to right also. The page you just dropped in place will be numbered with the previous section you have set up (so in my case, it becomes page 4).
Now, there was one funny thing that happened. I had a red box on my left master, and a blue box on my right master, just so I could track the pages visually. The page number was on top of the colored box. When I added my new page 4, the colored box on page 1 (the real page 1, not the new section's page 1) jumped in front of the page number text box. I removed the new page 4 and then dragged a new one where the old one had been, and page 1 went back to being correct. I'm not sure why something upstream should have been effected by adding a page downstream, but maybe someone else can see if they get the same results.
Anyway, that's a workaround that will save you from having to drag all of the pages to the correct side of the spread manually.
EDIT: I should probably add that changing page 4 to page 1 isn't something that I would normally do. Whether or not you want a new page 1 in the mix, there needs to be a page 4 of some sort (whether it has content or not), so if I had wanted what was on page 4 to become a new page 1, I would have probably added a new page 4 first, then created the section start on page 5. You get to the same place either way, but it helpes keep me straight when I work this way.