If I enter a search term in the quick search bar that corresponds to a project name, then select a project from the drop-down and search again, the search results are not filtered by anything.

For instance say I wish to search for the term "stream" in the JST project on studio.atlassian.com. I enter "stream", and get some unwanted results from the DEMO project. I then select "JIRA Studio" from the project drop-down and click "Search Again". The results are now completely irrelevant, and the search term "stream" has not been used.