Fonts appear different on co-workers version of Illustrator

I believe Illustrator substitutes fonts in when it can't find the one originally used, so at a guess I'd say that the fonts your coworker used aren't installed on your and the other coworkers' computers. Have your coworker make a list of the fonts in use in the files and on their system and make sure the same fonts are installed on yours.

If they are all fonts used through the Creative Cloud/Adobe Fonts, you can use the CC desktop app to see what is active on your system by opening the CC desktop app and clicking Manage fonts in the navigation panel on the lift. That will tell you all the Adobe fonts you have active on your personal system. You can click Browse more fonts at the top right to find the missing fonts if they are accessed through CC.

If you coworker used fonts installed in the Windows font directory, you'll need to copy the files to your own computer. If the fonts are licensed from a foundary, you might also need to get individual licenses from the foundary.

If you're on a Mac, I don't know where font information is stored.