A license generally affects you when you acquire, use, or distribute a piece of software that comes with the license. If you never acquire, use or distribute Evil Corp's version of your project, then there's simply no way any sane license they apply to it could possibly affect you.
Now, if they release a modified version of your project under a proprietary license, and you do something like incorporate their improvements into your permissively licensed version, then Evil Corp has every right to come after you for that. But as long as you don't do anything silly like that, you should have nothing to worry about.