Thanks for pointing this out, and sorry that it's not yet working correctly. We essentially ported the underlying logic from Old Search for these new messages since it was generally better than New Search's "A little more information" blue banner that was often incorrect and always too long for most people to read. Now that we're trying to be smarter about recommending what information should be added it's a little trickier than just using one generic message, so we're going to tweak and refine the logic in the coming few weeks.
Also, the search engine definitely takes into account all the fields included in the search form whether they're manually entered or pre-populated from a tree-search. Feel free to send me any links to searches that don't seem right, we're working to improve our default tree-based searches as well.