Submissive urination is a normal way for your puppy to demonstrate submissive behavior. Even a dog that is otherwise housetrained may leave dribbles and puddles of urine at your feet when greeting you. Excitement urination with a puppy is usually caused by lack of bladder control. The puppy is not aware that he is urinating; he's just excited and any punishment will only confuse him.
If you’re like me and have trouble keeping up with your pup at all times try using a tether. You can buy a tether from the pet store or simply do what I did and use a long lead or leash. If tethering your pup to you at all times is what it takes to make sure they’re not sneaking off then go for it. If you’re not keen on keeping your dog tethered you can use baby gates or closed doors to restrict your dogs access to the whole house.
It’s best not to punish the puppy for making a mistake. Instead, focus on praising appropriate bathroom behavior. If you catch your puppy in the act, interrupt it by saying “No!” in a firm voice or clapping your hands loudly, then take the puppy outside to finish going to the bathroom. Never swat your puppy, yell at it, or try to rub its nose in the mess.