Tervingi/Visigoths were less a nomadic/semi-nomadic people than a largely autonomous Roman army, made of Barbarian or "Barbarized" Romans : meaning that you'd have to expect the same logistics involved in most mobile but garrisoned (trough civilian lodging and supplying) Late Roman armies : reliance over imperial wages, subsides or gifts; and barring that, plunder.The materials (gold, silver and garnets are, up to the VIIth century, essentially coming from Constantinople trough subsides or gift-based diplomacy; at least from the supply, Barbarians depended from imperial logistics as a whole.

It's less clear when it comes to production : indeed, the difference between an "ethnic"-looking ring or broach made by a Roman or a Barbarian is hard to distinguish to say the least, the style telling more about the backer and the clients than the maker; and while you certainly had a Barbarian style, there's not enough room to define a Barbarian "craftsmanship" distinct from Romans and it's quite possible that a significant part of early Gothic jewellery was made in eastern Roman cities, particularly Constantinople.

For the pieces that wouldn't be, as Barbarian rulers were as much king of their people and Roman generals participating to late imperial society, they had access to goldsmiths and silversmiths of occupied provinces and cities, in relations with local Roman elites Barbarian dealt with. It's really with the Vth century and the creation of stable Barbarian palatial ensembles in imitation, then replacement, of the Roman state that it might be safe to consider a Barbarian craftsmanship more or less independent from imperial purveyors (although Constantinople continuously supplied Barbarians with precious gifts and supplies to be transformed until the VIIth)