There were also a number of French Tullies in my family, and I can trace it back only so far as a spinster daughter of my 4th G-Grandmother, who was b. at the end of the 18th C.
Tullie and Tulita were her nicknames. Her niece and a number of other descendants were named "Marie Antoinette" in combination with other names and nicknamed "Tullie" and it seems to have become a given name along the way.
I think it is quite beautiful!