You are right. The Tomasi family is one of the most ancient Tyrolean families. The name is probably a derivative of Thomas, through the Latin genitive (patronymic) Thomasi. The languages spoken in Tyrol are German, Italian and Ladin (a rhaeto-romance language with celtic influence), therefore the Family's heritage can be traced throughout history following the migrations of Germanic, Celtic and raetic people in the Alps. Depending on the time and spelling (also due to the forced Italianization of lastnames by Hitler and Mussolini - see Ettore Tolomei), the last name can be found as Tomasi, Thomasi, Thomasii, Thomasij, Thomas, Tomaser, Tomazer, Thomser, Thoma , Thome, Tomasson, Thomson, Thomsen etc.
We have to pay attention: Tomasi (with one 'm') is the Tyrolean/Nordic Family, while the Tommasi (with two 'm's) are a original family from central Italy.
There is also a noble Tomasi family in Central and Southern Italy, who, according to some, dates back to the 4th century BC is Bizantium, Eastern Roman Empire, who came to the Italian Paeninsula around 640 AD. Its lineage is related to the "Leopards" of Giuseppe Tomasi di Lampedusa, and through him to the Baltic branch of the Family. We don't know for sure if those two Tomasi families are related. In Tyrol, the Germanic influence started with Germanic tribes such as Bajuwari, Alemanni, Cimbri, Teutoni, possibly from Scandinavia (in particular the Danish Jutland); in Sicily the Germanic influence was carried by the Northmen.