What likely happened is that when you put in your child’s income, TurboTax claimed the Canada Workers Benefit (CWB) (aka the Working Income Tax Benefit) for them. 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 when you added your child’s tuition, then the CWB was removed, lowering their refund.
If your child doesn’t need all of their tuition for their own return, then they can transfer the amount to you. However, the tuition transfer is non-refundable, meaning that it can only be used to help lower the amount of tax that you need to pay. So if you have no taxes owning, then the tuition transfer will not change your return.