Two things are necessary to understand what Jesus did at the marriage feast in Canaan.
1. "Wine" in the bible does not mean exactly the same as we use it today. "Wine" was a common beverage served at meals and other social gatherings. "Wine" was beverage alcohol mixed with water at usually 4 or 5 parts water to one part wine. This was done for two reasons. First was to purify the water of any pathogens that could cause illness. The alcohol killed the germs in the water. The second was to avoid drunkenness.
2. "Strong drink" was when wine was served straight without mixing with water. The distilling of wine into brandy did not occur in Europe/western Asia until the 12th century AD. As wine did not travel well (the shaking mixed the sediments into the wine making it bitter) the practice in the middle ages was to distill the wine into brandy, then, when it arrived at its destination, to mix it with water and drink it. As time passed many people began to prefer the distilled spirits straight without mixing. But even today, "mixed drinks" are more popular than straight brandy, whiskey, gin or vodka.
So, when the wine ran out, or was "well drunk" Jesus took water jugs and turned the water into wine. My assumption is that he turned the water into the mixed wine which was usually served on such occasions. Alcoholic? Sure. How much would you have to drink to get drunk? More than your stomach could hold!