Hmmm, I don't think it's strictly normal. My 6-year-old sometimes gets a bit moody and difficult. Tiredness, changes, stress, all make it hard. I suspect this 6-year-old maybe has extra pressures, with his mum not being around?
I think what you did was probably sensible. I would have stressed, maybe, that you like him but can't cope with the behaviour, and he needs to calm down, iyswim - make clear it's the behaviour and not him that's the problem.
Actually, thinking about it, the fact he did this with you was curious - does he do this with his dad? They normally save their worst behaviour for the people they know best ...