Rules-as-Written, the Jug can sustain up to 5 players
The Player's Handbook has explicit rules about food/water consumption you'll want to reference.
A character needs one pound of food per day and can make food last longer by subsisting on half rations. Eating half a pound of food in a day counts as half a day without food.
A character can go without food for a number of days equal to 3 + his or her Constitution modifier (minimum 1). At the end of each day beyond that limit, a character automatically suffers one level of exhaustion.
A normal day of eating resets the count of days without food to zero.
A character needs one gallon of water per day, or two gallons per day if the weather is hot. A character who drinks only half that much water must succeed on a DC 15 Constitution saving throw or suffer one level of exhaustion at the end of the day. A character with access to even less water automatically suffers one level of exhaustion at the end of the day.
If the character already has one or more levels of exhaustion, the character takes two levels in either case.
—Food and Water, Player's Handbook, pg. 185
An alchemy jug is more than capable of producing a gallon per day (up to 8, in fact, of fresh water), and there's no rule that fluids produced by the alchemy jug vanish over time, so in a temperate climate, an Alchemy Jug could produce enough water to sustain 8 humanoids, meaning the excess can be put towards food instead.
A Humanoid must consume at least 1 pound of food to stay nourished, and an Alchemy Jug is capable of producing 1 gallon of Honey, 2 gallons of Mayonnaise, 4 gallons of beer, and 1 gallon of wine. 5th Edition D&D doesn't have rules about Macronutrient balancing, so at least per the rules of the game, 2 gallons of Mayonnaise (or about 16 pounds) is enough to sustain up to 16 creatures per day.
So realistically, a party of up to 5 characters could subsist on nothing but an Alchemy Jug, producing water 2 of every 3 days (5 × 3 = 15 gallons of 16 gallons produced), and producing Mayonnaise every third day (5 × 3 = 15 pounds of 16 pounds produced), with an excess of 1 gallon of water and 1 pound of mayonnaise every third day.
So unless the party is bigger than 5 humanoid creatures, there's no need to call for any kind of checks in the first place. They are fully capable of keeping themselves fed and watered.
So what can you do about it?
I mean, you have to take the Alchemy Jug away if you intend to run a proper survival campaign.
Even if we rule that only the water is nourishing, and that surviving on Honey/Mayonnaise/Beer/Wine doesn't provide enough nutritional value to subsist on (which, if you're running a survival campaign, is not an unreasonable houserule to implement), water is easily the much more difficult substance to obtain. Literally, professional survival guides in the real world emphasize the securing of water to be the second priority, coming only after securing safe shelter from predators/the elements. And in the mechanics of the game, going a single day without water (or even substandard water) is far more taxing than going several days without food.
So an item whose only purpose can only ever be to trivialize that part of the difficulty is always going to be a problem, irrespective of any attempts by the players to also let that item sustain their food needs.
So if you intend to properly restore the survival mechanics of your campaign, you're going to need to remove that item. Talk to your players, explain the issue (and make sure you're all playing the same game), and then, having done all that and having gotten assent from your players, contrive a narrative justification for why the jug is gone or doesn't work anymore.