The reason you may not see data for metrics such as clicks and conversions in Ad Extensions widget which is present in AdWords is because AdWords reports this data for All Extensions, it is not just for a specific Extension.
The clicks that you see by default against the extension are for any click that happened on the ad when the extension showed. This is the case with other metrics as well. The data you see in the reporting widget in Optmyzr is for that specific extension. It is possible to see this data in AdWords by selecting the segment 'This Extension vs. Other'. That will show you how many clicks that extension actually got and how many clicks other extensions got when this extension showed.
In AdWords, you can segment the data and the numbers you see for 'This Extension' should match what you see in the Optmyzr widget. The reason we show data in this manner is because the numbers you see in AdWords under the default setting can be misleading.
Our award-winning customer care team is here for you.