The "Ubi tu Gaius, ego Gaia" marriage vow will also be said when the bride arrives at the groom's doorstep. There is occasional mention of a bride using her groom's actual name as well as the traditional "Gaius," but I'm not sure how apocryphal that is. So, let's say this is Iusta's own personal elaboration on her vows.
Now, hold still and smile for the fresco artist...
The "Gaius and Gaia" formula was an ancient tradition. One could substitute the groom's name, but saying "Gaius" linked the bride to a story of a virtuous wife from the earliest days of Rome, who declared herself one and the same as her husbandwhose name happened to be Gaius. Many elements of the traditional marriage ceremony recalled early Roman history, as well as symbolising the transfer of the bride from her parents' hearth and gods and ancestors, to those of her husband.
There was a more complex ceremony when members of the patrician nobility married in a way that would qualify them for priestly purity. And after that, the restrictions on what they could wear, touch, where they could sleep, even where they could walk became extremely complicated. Mus has an entirely different set of rules to worry about.