The preview estimate of mentions works the same way as the historical estimation of mentions. What NUVI is doing is running a quick CONTAINS statement to Twitter. This contains statement will return results of mentions that CONTAIN the keywords/author_usernames that you are searching.
This quick CONTAINS statement does not filter down every mention listed in the Preview to contain ALL these words or take into account your exclusions. This is why the number might be more than what is being pulled into the monitor. If you have a Map Region in your ruleset that will also narrow down your results once a historical is pulled. Once historical is pulled on the monitor it will go in and match all your rules against the results and mismatch data. These mismatches will account for the large gap in numbers in the preview and historical.
If you have fewer results than expected in your monitor after pulling a historical. Here are a few things to check.
First, make sure that your rules are set up correctly in your monitor. Sometimes you can select ALL instead of ANY and this will narrow down your mentions quite a bit.
Also AND statements instead of OR statements can narrow down your searches even more.
Geo filters such as Map Regions and Locations can narrow down your results as well.
Another trick you can use is to compare your ruleset to what the Preview is showing. NUVI allows you to select the mention and view it in its entirety on Twitter by selecting the Time/Date of the mention.