Wow, this is a very unusual situation. The latest version has been downloaded dozens of times and this is the first issue that has been reported.
So you are saying that when you extract osTicket-1.12.2-Awesome-101.zip to your computer, the /osta folder is missing?!
Do you get any error messages when you extract it?
I would offer to take a look or even upload the files for you, but as you are on a private network this will not be possible.
If you send an email to info@osticketawesome.com I will reply with a Dropbox link to the archive. Maybe you’ll have better luck downloading it from another server.