Tea Masters House Won't Unlock

Providing the game tells you that you've served "26/26" teas, then the house should have unlocked

So, open the trunk, tap on the Tea Set and check the count at the very top of the screen

The 'task completed' icon in the trunk would show Layton and Luke sitting in a tea cup inside a case

Keep in mind that characters become randomly thirsty and you'll need to visit every person that you're not sure about then run in and out of their location, say, ten times (although, being random, it can sometimes take closer to twenty times) to see whether they will become thirsty

This is discussed further in this FAQ
http://professorlayton2walkthrough.blogspot.com/2009/08/faq.html

This popular walkthrough also has a Tea Breaks index down the right side that will show you where everyone who needs tea can be found along with which tea they want