Do toddlers hit themselves when angry or told no?

We don’t do corporal punishment. We do time outs where we sit him in a corner and if he moves he sits in my lap and I hold him down for 5 minutes. Usually this would be after the third no. He is 1 year 9 months but recently whenever you tell him no, he just starts hitting his head with his hands and if really angry then bites his arm. The daycare he is at has cameras and from what I have seen, they just sit them in a chair in the corner when they did something they shouldn’t have (bite another kid, or hit them or take someone’s toy, etc). I don’t know where he might be picking that up or if it is just frustration and he cannot express it any other way. 90% of the time he is well behaved and playful so it is not often we need to tell him no or take a toy away. Is this some stage of development style behavior? He is only child.