They seem to have mysteriously disappeared... I'll assume that it was just a minor lag in their application or maybe as part of their "Under Construction" parking DNS, they relay some traffic to these random sites. However, now that my new DNS information has propagated through, everything seems to be fine. Sorry about the false alarm.
As a side note, I don't think Network Solutions provides the raw zone file or any raw DNS configuration file when customers use its DNS Manager. All of the work, I guess, is meant to be done through their web application.