My initial sympathy was tempered when it became apparent they used megatrain to book, this discount sales channel makes it abundantly clear it is a discount operation with strict T&Cs.
That said, I still morally think SWT are in the wrong, assuming the travelled on the service they booked tickets for, and it makes a scheduled stop (or indeed an extra stop) at the station in question, hard to make a case for any 'penalty' element at all.
And while there is a case for making them buy new tickets, a common sense operator should have just charged them the cost of singles from Southampton to Eastleigh.