There seems to be a bug in the date filter between Advanced Mode and the Date Range pulldown on the main search site interface.
In the Advanced Mode, under "Then narrow your results by…" there are two "date:" fields: Before date, and After date. This implies that Before date should be used to find results before this date, and After date implies it should filter results to only those after this date.
In the main site interface, these fields have reversed meanings. Using a Before date in Advanced mode ends up being the From date in the main interface, which is not what before means.
It looks like Before date actually means From date and After date means To date.
It's tricky to correctly set the date range to find results before a certain date.
Screenshots demonstrating this:


Setting Before date should return results before that date, not after that date. This is the traditional meaning of the word before.
Similarly, setting After date should return results after that date, not before that date. This is the traditional meaning of the word after.
The terms should be the same in both interfaces if they are supposed to mean the same thing. Using different terminology for the same concept in different places is confusing and makes it difficult to predict what the outcome will be.