I have cleared my cache. What is weird about it is that if you run through it one time it works okay but the second time it brings up the pop-up window. I am curious, please follow these steps and see if it still works okay for you:
1. Identify feature then close popup window
2. Use the measure area tool (at this stage everything works fine)
3. Close measure tool
4. Identify feature then close popup window
5. Use measure area tool
At this point for me the popup window activates when I click inside the polygon to measure the area.