Is it true that when someone gets married they are automatically added to the title of their spouse's house? 

No. The mortgage is a contract. That conteact is between the parties that entered into it. So, it is not automatic. 

That said, over time, the spouse can end up having an interest in the property over time. This is because marital funds can be used to pay the mortgage, bills, taxes, etc. 

Hope this helps.