Rupert is 15 weeks old and has been clean in the house for a few weeks now

He sits by the back door every time he wants to go out to wee/poo.
However, at night he is shut in the kitchen and sleeps his crate with the door open, its not a big kitchen! We take up his water around 8pm he is normally fast asleep by 930pm. We take him out for a wee then put him into the kitchen for the night
We put some paper down on the floor and when we get up in the morning (630am to 7am)he will always have weed on the paper. Occasionally when left in the day (for no longer than 2 hours) he will have weed on the paper.
When should we expect him to not do this? Are we confusing things by putting paper down, should we be cleaning up straight from the floor? Its tiled so not a problem if so

thank you!