Your name consists of the two parts Thall and Man. The second part is clearly an obsolete or Americanised spelling of Mann, German for man. As you will no doubt be aware, it occurs a lot as the second part of German surnames. The first part is trickier. There is no related German word with double l. There is, in particular, no German word even remotely similar that means tall. If you look at the etymology of tall, you will see that what you have been told just isn’t plausible at all.
However, there are plenty of German speakers (all over the German-speaking area) with names such as Talmann, Thalmann or Thälmann. It is not at all unlikely that the name is related to Tal, the German word for valley or dale. It was once spelled Thal. The word can possibly be understood literally (as in: one of your ancestors lived in a valley or at the foot of a mountain, and this was for some reason remarkable or in contrast to others). In principle it might also refer to a specific area related to a mine that was also sometimes known as the Tal, but I think this doesn’t really fit the name’s wide distribution.
One thing that seems to support the valley connection is that there are similar names in other languages, e.g. van Dalen in Dutch, Lavalle and de la Vallée in French, Della Valle in Italian, all meaning of the valley or the valley. Talmann is the most plausible German analogue of these names that I can think of. An English equivalent is probably the name Dale.