Advanced search fields taxonomies

Hello, in the listing page I have created a taxonomy multiple checkbox. Whenever I check some boxes while creating a profile, and afterwards I look for these options with the regular seach or advanced search, they are not found, unless I first check them myself in the back-end at the right off the page in the taxonomy I have created. Is this normal? If someone ticks off a box, shouldn’t that option be found in the search field? Thanks