That sounds like that might be the culprit, however, even with the AJAX function turned on in the plugin, I fully tested on IE9 with the Twenty Twelve Theme and all other plugins turned off, the calendar simply refuses to load the correct month AFTER the choice was made in the data picker and hit the “Find Events” button.
What it actually was show the same month before, because it failed to process and load whatever the month that was requested for.
-Josh