The tuition tax credit is offered by the Federal government as well as some provinces specifically to the student, regardless of who actually pays for the tuition. But, if the student doesn't use all the tuition, then they may be able to transfer part if it to a spouse, parent or other family member.
As to why his refund went down - what likely happened is that when he put in his income, TurboTax claimed the Canada Workers Benefit (CWB) (aka the Working Income Tax Benefit) for him. This is a refundable tax credit for people who work, but don’t make very much. However, students are usually not eligible for this credit, so tuition was added, the CWB was removed, lowering the refund. Other credits might be affected as well, as the tuition credit must be used before other credits, like the dividend credit.
If your son doesn't enter his T2202 on his return, he will not be able to transfer or carryforward his tuition. He may also have difficulties with the CRA if he takes credits the CWB when he is not eligible for it.
