Whether you are using Internet Explorer or not, you need to keep that browser as up-to-date as possible because other components on your system are using it. You’re absolutely right to do that.
But what you’re seeing now are called pop-unders. Unfortunately, I don’t know why updating Internet Explorer would cause things to pop up behind your windows. All we can really do is take a look at some of the possible causes for what you’re seeing in general.
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What are pop-unders?
In the early days of advertising on the web, you’d see banner ads on web pages. Then, some advertiser got the bright idea of having an additional window pop up to display an ad. Eventually, that caused pop-up blocking software and similar features in your browser to become mainstream.
To get around this software, some sites are now using pop-under windows. With these, you visit a website and a new window appears behind your browser, so you don’t see it right away. In fact, you continue browsing and then when you minimize the browser or close the window, you finally see the advertising in that pop-under window.
So advertising is the number one cause of pop-under windows. For a (very short!) while, I used an advertising service that didn’t tell me that they used pop-unders on Ask Leo!. That relationship didn’t last very long because I really, really do NOT like them, and I suspect that you don’t as well.
The problem with pop-unders is that some pop-up blockers don’t block them. I don’t know what to do about that.
I presume that your pop-up blocker is enabled in your browser. If that’s not blocking pop-unders, that makes it difficult to suggest a solution other than not visiting sites that use pop-unders. Of course, you don’t see them for a while so it’s not always obvious which site it using them.
Single-click versus double-click
Another thing that comes to mind is whether you’re single-clicking or double-clicking the link. When you see a link on a web page, you click it once to go to that page. If you mistakenly double-click the link, it’s possible that the first click opens a browser window and then the second click causes your current window to come to the foreground. The result is that current window remains in front of whatever it is you just clicked.
The fix, of course, is to make sure that when you’re clicking links, you click them only once.
‘Always be shown on top’ settings
I have one more theory about how this could be happening. It actually is possible for programs to tell Windows that they must always be shown on top of other Windows. In fact, there are even some add-ons that allow you to apply that functionality to any window. But you would have to have downloaded and installed one of those to make that work.
But if you have a program that automatically forces Windows to do this, it can be annoying unless the program is doing something really important. Nonetheless, it could be another reason why you are experiencing this problem.
I don’t really have an answer to why it’s happening to you after your IE 10 upgrade, but I wanted to cover at least some of the basic ways that windows can show up underneath your current window.