Tertius, tertia, tertium is an adjective, meaning "third." The noun "cliens" is masculine, so with the adjective, it becomes "cliens tertius." So the third client is in the building.
However, I can't guarantee that this couldn't be interpreted with a nominalized adjective, in which case your interpretation would actually be correct. I'll let someone else weigh in on this for the time. :)
Volgav vitsenanieff nivya kevach varatsach.
I think that would most likely translate to "the client in the building is the third", because of how in aedificio is placed.
My Latin is a bit rough, but if I remember correctly, tertius generally goes with a noun unless it's placed without a noun before or after it, so you got that right.
A "customer" would an "emptor". I've learned that in the other lessons. Even if "emptor" means literally a "buyer".
A client here, means someone who is dependant of a protector (patron).
Click on "reply" to have your answer above the question. They didn't see your answer.