Not sure what a tatami is, but nope my kids don't sleep on futons that are on the floor. We got dorky toddler bed for my 4 year old. My daughter 7months sleeps in her crib/playpen. My son started sleeping on his own bed at 1 years old. We put up a child gate in the doorway to keep him in his room. If he woke up he'd go to the gate and cry, and I'd get him.
Not sure if that in anyway answers your question..