How is one supposed to stop Chromium processes?

I had the same problem. Turns out this is a feature of chromium/chrome where it leaves processes running for extensions. To turn off go to Settings-->Show Advanced Settings-->Background Apps and uncheck the "Continue running background apps when Chromium is closed" option. Reference: https://superuser.com/questions/269385/why-does-google-chrome-leave-running-processes-behind-even-after-closing-the-bro

You can terminate it from its built in Task Manager

right click on tab and choose Task Manager then choose the process you want to kill(in your case you would kill all processes then you can close the browser)

Note that images are taken for chrome not chromium but its the same "nevermind".