Technically, Rita says an incantation before doing a spell. For Tidal Wave, she says "O mad and greedy waters, rise up and storm the very heavens; Tidal Wave!". However when she's in Overlimit, she can instantly cast spells. And as a result... "Blah, blah, blah... Tidal Wave!"
The Milky Way (weapon) allows her to not get interrupted during spells, which has always been the most important skill that a mage in Tales games can get.
So they're not exactly related but sorta. It's just that Rita is broken once she equips the Milky Way since she can get to Overlimit quickly and then spam Tidal Wave for Grade/Money farming.