When your adult reaches the age of 6, there will be a new location under the door icon called "Date Place." That's where your Tama goes to get married.
So you need to wait 3 days from when your Tama evolves for him to be 6 so he can marry.
Hope I helped!
Edit: your Tama won't have a baby right after it gets married. The mate goes and lives with your Tama for a while and on the second night, I think, they will have an egg that will hatch.