The problem here is that pop-ups come from many, many different sources and may be of many different kinds. Some are the very legitimate price you effectively pay for viewing a free website, others not so much.
No one likes pop-up notices and advertisements. In your case, it’s difficult to be specific about a solution because fixing this depends on exactly what ads and pop-ups you see, what they look like, and how they appear.
Because there are so many potential sources for pop-ups and advertisements, I’m going to review some of the most common and hope that one of them will apply in your situation.
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.