Yes, a US plant is a necessary pre-requisite to not have import tariffs on the finished vehicles.
I would not make the link that BYD == "super-cheap cars"
BYD Han, EU price €69,990. High price.
BYD Seal, EU price €44,900 and up. Not cheap, lower-middle of the pack.
BYD Dolphin, E Price €29,990 and up - that's at the cheap end. But not "super" cheap.
BYD Sea Lion, coming soon, around €24K / USD $26K maybe?
BYD and other might (and hopefully will) go below €20K / USD $25K into the "super-cheap" category. But that's hardly the whole of or current reality of the brand.
Your video link has the title calling the Han a "luxury Sedan" so I don't know why you would talk about "super-cheap", or invent concerns about model name longevity.
YEs, BYD seems likely to be _in_ the super-cheap category. So will others.