Correct, and yes it does apply to vintage lenses. A lens doesn't know or care what's behind it, new or old.
So if people say to get a "50mm equivalent", and you're using a MFT camera, you'll be looking for a 25mm lens. A 50mm on MFT would produce similar photos as a 100mm would on full frame, etc.
The a6000 is a fantastic camera, and is APSC as opposed to being MFT, which means a larger sensor, and all the benefits that come with that.
That also means it'll be a bit larger as a camera, and any camera will be a considerable step up from a phone, but just fyi