That doesn’t happen here. I don’t currently have any January events entered at the development site where I have EME 3.2.12 installed. However, I have a February 24th event. The December calendar displays December events. When I click the right arrows a January calendar displays normally, but without any events. When I click the right arrows again a February calendar displays showing the February 24th event.
I am displaying the calendar by means of a shortcode on a WP page. Maybe the problem you are having is unique to use of the calendar widget or is a theme issue if you making a function call from your theme. If you are not using a shortcode on a page, I suggest that you try that method as a test to help troubleshoot problem, because that method works for me.