This doesn’t mean that the people are sinning during the millennium when Satan is bound for that time does it, but that after his release he is able to convince man to sin again, as he did Eve in the garden? And he will be released for a time, which could be quite a period of time, as in the days of Adam to Noah, it didn’t take long for the whole earth to become evil.
Yes, I’m afraid it does means that on Earth there will be sin in the Millennium. That’s why there will be daily offerings for sin in the Temple right from the beginning (Ezekiel 46:13). In the most personal sense, it’s not Satan that causes natural man to sin, it’s natural man’s sin nature. I believe that one purpose of the Millennium is to demonstrate that there are no circumstances under which natural man can live a life pleasing to God. All Satan does at the end of the Millennium is to organize and lead the rebellion against God that will have been building in the hearts of men all along.