So, I did some tests, and the problem arose in Chrome too. Until you click the tooltip that Chrome is working and IE is not working.
Digging deeper in this question, it seems that both browsers do not recognize the mousemove event when you scroll. Therefore, if you hover over any browser, then scroll down or up, the tooltip will remain. When you click the tooltip in Chrome, the scrolling then fires the mouseevent, which apparently fires the mouseout / mouseenter. In IE, it does not add a scroll trigger. Actually, this may not be a problem with the browser, but a way to load the boot file when you add this extra scroll trigger, just like mousemove.
To test it yourself, try adding a mouse move event to the console for bootstraps / tooltip.js
$(document).mousemove(function(event) {console.log(event);});
Mouse movement should trigger events in the console. If you hint and scroll away, it will still remain. Then click the tooltip and notice that now scrolling fires the same mouse event in Chrome, not in IE.
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