Every contractor wants to be last. But common sense says all demo should be completed before any painting.

I would remove all the doors/drawers from existing cabinets and then remove the tile floors. Paint cabinet boxes. Install floor. Install repainted doors/drawers (which hopefully have been repainted off-site).

This was tile removal in my previous house ...

I agree painting last and if the painter can't do that get another painter. The caibets need to be done in a spray booth not on site the whole kitchen IMO needs to be installed including floor before you choose wall color . Tile removal makes ahuge mess so the comment about removing doors and drawers is totally right . That would also be a good time to send out all the doors and drawers to the paint shop.. If your contractor can't work with those perameters you need a new one .