You physics isn’t really inverted, it’s just doing the opposite to what you expected 
, but it is quite correct.
Edit: Cut for clarity, I think the cable car analogy is easier to understand.
For cornering think of a cable car suspended from a wire (where your wheels are) - it swings out, tipping the top of the car into the centre of the curve - the opposite of a normal road car, with its mass above ground, which rolls out away from the centre of the curve.
Your 1920s tyres will have less grip, but the cars are narrower and their CoG higher - I believe they were still inclined to slide before roll unless they hit a trip.