I don't think you can do anything for the moment which was part of the discussion in the other thread...I'll try to see if I can find that link. Apple did not properly implement the Background Apps feature before release so now users are stuck with these issues regarding Background Apps. It will likely take Apple a while to fix this feature assuming they even know about or care about it...obviously they didn't care enough to hold it back from a production release.
Contact the developers of the affected apps for assistance, but like I said, I don't think they have any information about how this new feature works with their apps so it will likely take them time to figure out what will prevent unnecessary notifications.
You can provide Apple with product feedback here (Apple won't respond):
Product Feedback - Apple
Edit: If you don't use apps from those developers, then uninstall them by following the developer's instructions. Sometimes downloading apps from a website will also include other apps hidden or bundled into the installer for the main app.