Welcome to Universe 15-A! Or was it 15-B? Aw, heck, there's so many different Sonic universes out there I can't keep track of them all! But here's how this one operates, so listen up!
I'm drawing inspiration from a lot of different sources, mostly from the "Bizarro Universe" trope. Everyone from Sonic's reality is here, but inverted. Good guys are bad, bad guys are good, nothing is the way you remember it. To quote Wario: "It's-a good to be bad!"
Rouge's personality is a combination of canon Rouge, Bunnie Rabbot, and Applejack from My Little Pony. (And just a little bit of Mario.) She's still a big flirt and a sucker for anything shiny, but also a country sweetheart with a big heart to go with her big... um... ears. Yeah, ears. That works.
Hey, You Got Your Sonic in My Mario!:
I love crossovers, so bring me whatever you've got! By default, I accept the Mario and Sonic universes coexisting, which means Rouge and Mr. Tinker most likely live in Wario World. Don't be surprised if a pair of creepy pointy-eared trolls with Italian accents show up somewhere.
Ain't I A Stinker?:
Both Super Mario Bros. and Sonic the Hedgehog were inspired by classic cartoons like Popeye, Mickey Mouse, and Bugs Bunny, so the same goofball antics apply here. Besides, Looney Tunes logic is the only way to explain how Sonic can spin dash, Tails can fly, or Rouge's back can support those... ears. Definitely the ears, nothing else abnormally large on her or anything.