I'm making a plugin that lists the colors and their corresponding color code, and i need to know how to make it alert those with a specific permission that an update is available
Read the entire instructions. You need to copy the whole Updater class into your plugin. It'll all there, read carefully.
There are a bunch of projects using it that you can reference if you need help. Find some by searching github: https://github.com/search?l=java&q=net.gravitydevelopment.updater&ref=searchresults&type=Code