Ideally, it's better to output each page as if they were separate pages with their own bleed.
The reason why: magazine don't have the same thickness and when the printer does the imposition work, he needs to calculate the "creep" (How can I determine how much bleed to use?). When each page has its own bleed, the printer has a bit more freedom in how they will apply the creep.
It's not a big issue when your 2 pages actually share the same image/background but it can give ugly results with 2 different pages as shown in your example.
- Separate your pages so they don't share the bleed but have all their own 4 sides bleed. You can slide down each page in the page layout so they're not facing anymore and then open the bleed where it's missing. Make sure to groups together the elements on the page, sometimes some elements will not follow the page when you do this.
(Very good url suggested by Joonas: http://indesignsecrets.com/breaking-pages-apart-to-bleed-off-a-spine.php)
It's alright to work with facing pages when you're doing your layout, it helps having a good idea of the final result. But it's true it makes things complicated when it's time to prepare the print-ready file and it's almost necessary to always split the pages once the design part is done and approved.
One technique you can use to avoid doing this is to work as single page with 4 sides bleed, export your PDF and then create a "proof" Indesign by importing the PDF pages where the pages will be facing. There's less risk of mistakes this way and you'll always have your print-ready file ready to export once the project is approved. It won't require to do any extra manipulation therefore less risks of last minute mistakes!