Two of my dses are currently at university, and the eldest has graduated, so we have done the whole 'first time away from home with money burning a hole in the pocket' thing three times, and only ds1 managed without going over budget.
Ds3 miscalculated last year - he thought he had one more SARS payment (the Scottish body that awards student loans), than he actually had coming - which threw his finances completely out, at the end of his first year, so he was pretty broke over this summer. We had given him a bit of cash at the end of term, so he could feed himself, but that was it - we didn't give him money for entertainment over the summer.
Instead he got work with friends of mine, labouring for them - and had to work damned hard for his money - and that was a good lesson for him. He won't make the same mistake next year.
Ds2 went overdrawn during his first year - and left a mini bank statement detailing the overdraft on the kitchen table, which is how we found out. We were able to give him one of his parental contributions a bit early, which sorted him out - but dh sat him down and gave him a stern lesson on budgeting.
Dh did give them all the budgeting talk, before they each started at university, and we did our best to give them the tools they needed to be able to budget their money properly - but two of them made mistakes - and frankly I wasn't entirely surprised at that - it isn't easy, being away from home for the first time, with more money than you have ever had before, and far more freedom too - as well as a thriving social life, and lots of people the same age as you to share that social life with.
When I was a student nurse, back in the '80s, I wasn't on a grant - I was paid - but I still cocked up my budget from time to time - we all did, to a certain extent. In fact, we used to get paid on the last Wednesday of the month, and we all knew that, if we wrote cheques the preceding weekend, they wouldn't be cashed until we'd been paid, so we wouldn't go overdrawn. That weekend was commonly known as Cheque Bouncing Weekend!
The OP's son has cocked up - but it sounds as if she has a plan to help him get through until his next payment comes through. Hopefully he will have learned his lesson, and will not make this mistake again.
I would advise the OP to sit down with her son and go over his budget again - look at income and any fixed costs, and work out how he divides up the rest of his money to cover essentials (food, books, transport etc) and luxuries (entertainment, parties etc). I always used to struggle with budgeting until I learned to divide up the money that was left after the fixed bills went out so there were separate, smaller budgets for all the other things, and I could see easily if I was overspending on food, or books or whatever - maybe that would help the OP's son.