15 minutes is too long for a 16 months baby, I think.
Here is the suggestion: maybe u can try 2-5 minutes, leaving the baby to safe and quite place (which you use often to discipline him, don't use the regular place where he eat or sleep). But before doing so, try to understand why he is crying. Usually there is a reason. Try to learn/understand his cry.
If you really conclude that he 發脾氣, then you needs to be very calm (and use short sentence) tell him that you'll leave him 2 - 5 minute to calm down (and sure he'll cry harder as he might think you do want him).
When you pick him up, be calm and take him sway from the discipline area and talk to him again calmly, try to understand he is crying and repeat the above step.
I had brought a book , named Magic 1-2-3 (cannot remember the exact name) works very well but it's for kids 2 years old and above. You can consider it when he is older.
No, you don't have to wait he stops crying. You just picks him up, talk to him CALMLY to see if he is actually slowing down the cry or 脾氣. If your routine is the same before putting him to the discipline area, then they should get it sooner or later.
You can put him to the discipline area. Then each time he is unreasonable, you can do it after talking to him, then to his discipline area. See http://lifeprint.com/
Teaching him sign language also can facilitate the communications like 'hungry', 'yes', 'no', 'drinking', etc...