'everyone' can be read as singular or plural. Like 'lego'. Mass noun or count noun. So you can have it both ways - everyone (the mass) can add themselves, or everyone (each component person) can add him/her/themself.
I don't believe in the word 'themself'. We don't have 'oneself' in that context, I reckon, because 'oneself' already has a first-person meaning and can't handle a third-person one on top of that.