You're running into Font Book's shortcomings. I'm guessing this is what's happening.
For about a minute, Font Book adds each font one by one.
If you haven't changed Font Book's preferences, the default is to copy the activated fonts to the Fonts folder of the current logged in account. This is important to remember for the next part.
BUT, if I login as another user they are nowhere to be seen.
If the previous statement I made is true, that's why another user can't see them. They've all been copied to the Fonts folder of a different user account, which no other user can access. Choosing "Computer" in Font Book allows use of fonts in the common /System/Library/Fonts/ folder, and the /Library/Fonts/ folder, not the entire hard drive.
One odd thing, is when I navigate to the downloaded font folio folder, I can click on a single font (not the folder, but the actual font) and select 'Install Font.' Do I need to do this first for every font (all 300+!!)?
No, but you'd just be repeating the copy of every font to the next user account, assuming you haven't changed Font Book's default settings.
To clear this whole mess up, do this.
1) Log into each user account and delete every font in that account's Fonts folder. Make sure you have backups of any fonts in those folders that do not exist anywhere else. Most likely though, they'll all be copies of your Adobe Font Folio fonts. Do not launch Font Book in any account.
2) If the fonts are duplicated in the common /Library/Fonts/ folder, delete those also. You want the Adobe Folio fonts in only the original location on the hard drive. Best place to put them is in the /Library/ folder, but NOT in the /Library/Fonts/ folder. You want them in a location where anyone on that Mac can activate them, but not in a folder where they are considered "on" all the time. You can also put the font folio at the root of the drive so its folder shows up alongside Applications, Library, Users, etc.
3) Reset Font Book for all user accounts. Login to each account in Safe Mode. Do that by restarting and immediately holding down the Shift key. When the login screen appears, enter the name of an account. Let it boot to the desktop. Then restart and do a Safe Mode start again, entering the next user account at the login screen. Repeat until all accounts have been started up in Safe Mode.
What this does is reset Font Book's database and clear all cache files for the account you logged into. Which is why you have to do it for each one. After doing a Safe Mode boot into the last account, reboot normally to any account.
4) Biggest part here.
DO NOT add fonts in Font Book in the usual manner. Use the New Library function. It looks the same as a new font set, but acts completely differently. Create a new Library and give it any name you wish. Then add your fonts to the Library. What Font Book does with a Library is it adds the fonts in what appears to be the same manner as a font set,
but it does NOT copy the fonts being added to the Fonts folder set in its preferences. They are instead activated in place. In this manner, everyone is always using the original fonts from the same location.