Massimiliano Vitiello's recent biography of King Theodahad from 2014 suggests that the future king was born in Novae in Moesia, rather than Tauresium. I have no idea where the evidence for Tauresium comes from, since from what I understand our knowledge for the Ostrogothic kings' background ranges from obscure to non-existent. Wikipedia does cite something, but it links to a webpage that is now unavailable. I found the link it should be directed to (here), but it requires a subscription to read, so unless someone has access to it, I can't really comment. Vitiello did mention this article in his book, but not in relation to Theodahad's birth, so presumably it wasn't important enough to be discussed or because he didn't find the argument for Tauresium to be that convincing. This book received reasonably positive reviews and no-one has criticsed him for his reconstruction of the king's early life, so I'm inclined to go with Vitiello on this one.

Anyway, Vitiello relied principally on a fictional letter written by Procopius, the (in)famous Greek historian of Justinian's reign, which possibly drew on genuine information available to the historian. This is as far as I'm aware the only biographical information available for Theodahad's early life:

I am no stranger to royal courts, but it was my fortune to have been born in the house of my uncle while he was king and to have been reared in a manner worthy of my race.

Based on this and snippets from other sources, Vitiello argues that Theodahad was born after 487, when his mother returned being a hostage in Constantinople. As Procopius claimed that Theodahad was born in the palace of Theoderic the Great, then he must be born in where the Ostrogoths were based at the time, thus Novae in the province of Moesia Inferior sometime in the late 480s. Another possibility is the 490s, but Vitiello prefers an earlier birth so that the ages of his sister and children makes sense (not a very solid argument in my opinion). In general the evidence is terrible and dependent on later authors mentioning, for example, that Theodahad was 'of mature years' when he became king, which is not that useful for writing a biography of the king!

Anyway, even if Theodahad was born in Tauresium, there is no reason to think that it was significant. Justinian was born a peasant, whilst Theodahad was the nephew of a Gothic king and the Roman consul of 484. They would have had no connections to each other even if they met as babies, simply because they moved in such different worlds. Beyond that, I'm not sure what there is to say, since coincidences are entirely subjective. Had Justinian remained a peasant, would you be surprised by the fact that he was born in the same place as a future king of Italy? I think that while the human mind is drawn to patterns, life rarely conforms to them.