I matter of fact that isn't true. Their physical form doesn't change unless they want it. At cursed level 2 as you said their whole body is covered in those marks, but those demon-like forms don't come automatically on activation of cursed 2 lvl.
So that i'm not talking bullshit you can check the chapters (186) where the sound nins confront the 2 jounins in the forest. They activate cursed seal lvl 2 when they're fighting and they look like humans at that moment. And a couple chapters (189) later that fatty nin activates that demon form against Chouji.