You can use mana generated by the last ability to pay an alternative cost (such as a dash cost) or an additional cost to cast a Dragon spell. It's not limited to paying just that spell's mana cost.

An activated ability appears in the form “Cost: Effect.”

Notably, turning a face-down creature face up isn't an activated ability. If you manifest a Dragon creature card or cast a Dragon creature card face down using the morph ability, you can't use mana generated by the last ability to turn that card face up.

The mana generated by the last ability can't be spent to activate abilities of Dragon sources that aren't on the battlefield.