My parents pay my tuition so will it help reduce their taxes?
Yes, that's correct.
Please see these TurboTax Canada FAQ for more info on how to transfer tuition in TurboTax:
How do I claim my tuition fees?
How do I transfer my unused tuition credits to someone else?
How do I enter tuition transferred from my spouse/partner or child
How much of my child's or spouse's unused tuition credits can be transferred to me?