The water to wine story is not an example of time dilation, and none of the miracles in the Bible have a relativistic answer to them. The possible exceptions are Psalm 90:4/2 Peter 3:8 which might be a frame of reference analogy, the creation story in Genesis 1, and Joshua's battle in Joshua 10:12-14. (Possibly 2 Kings 20:8-11)
Having said that, there's no way to know the mechanism for how God performs miracles. If we could explain them, then they wouldn't be miracles, only science.
Aging water for three months does not make wine, any more than a time shift can turn water into blood, which is the closest comparison elsewhere in the Bible to this miracle. In Exodus, Moses uses God's power to turn all the water in Egypt to blood. Millions of gallons of water containing fish and frogs (apparently lots of them) does not go into another time reference to change itself. God does it, whether it was instantaneous or whether it took some finite amount of time to our reference is irrelevant. Moses presence was incidental. He was just a messenger. Jesus through God just confirmed that God's power to manipulate things at a molecular level is absolute.
When he needs to change matter, he can. Arguing about whether you can attribute it to relativity is silly.