The LinkedIn search Icon relies heavily on the accuracy of your data. it is also very simple and easy to tweak in case your data is often inaccurate.
How it works:
1) It performs a "People" search, by inputting the First and Last name of your prospect into the LinkedIn search box.
2) It then adds the company name under "Keywords"
You can adjust either of these search methodologies within LinkedIn to get a more accurate result. However, if you don't see results, it may mean your data is wrong, and the contact either doesn't exist or had never worked at the company you are searching for.