bittrette - it seems like we are miscommunicating. Yes, the main purpose of EYB is to search for recipes in the cookbooks you own. To do that you search your Bookshelf not the Library. And if you have a lot of online recipes on your Bookshelf and only want to search in your cookbooks then you select the filter Book Recipes in the right side of search (or under the Filter link on a phone). I don't understand your comment "it shows the results from the Library rather than from my Bookshelf" - you select either Bookshelf Recipes or Library Recipes yourself from the tabs at the top of the site. Our search results will show what you select yourself.
I also don't understand your comment that searching by white onions shows the same results as "white onions". When I do those two searches of my own Bookshelf I get very different results and the search with speech marks around the ingredient only shows recipes containing white onions. This is those two searches in the Library:
Library Online Recipes search for white onions - 26,896 results https://www.eatyourbooks.com/library/recipes?q=white%20onions&online-recipes=true
Library Online Recipes search for "white onions" - 4,199 results https://www.eatyourbooks.com/library/recipes?q=%22white%20onions%22&online-recipes=true
The second search delivers very different results. Please email us with the URLs for the searches you do with and without the speech marks that deliver the same results and we can investigate further for you.