As an afterthought or technicality.
She took out a Denarian. Ramirez soulgazed her and she passed muster. If you wanted to bring in some indirect White Council politicking at this point, now's your chance, but don't do it openly. I think that understaffed as they are, the White Council would want all the help they can get. They also want to control powerful evocators like your PC there. To put on a show of divided fronts and political backstabbery right off the bat is counterproductive to their aims. Any WC personnel who show in an official capacity should likely do so as a united front, glad to have her help but not obsequious, and proud and confident in their own abilities and organization but not snooty (this last one is hard, yes).
The goal here from a selfish, cynical perspective is to get her under the WC's thumb, and if possible, arrange it so her primary contacts are isolated to (insert backstabbery political WC faction of your choice). That way they have time to groom her as a foot soldier/contact/loyal pawn rather than lose her to another faction. The "nice" perspective is that they're all in this together, and they represent, for her, an unprecedented chance to learn and expand her magical knowledge all while fighting the same evils she's already been fighting.
What they absolutely do NOT want is to reject your PC and have her so turned off by the experience she runs a risk of going black hat. Snatch her up, assess her, and kill her after you're sure she'll be a liability. Hell, she's one of the lucky ones, you know? Harry keeps saying how so many sorcerers don't even get noticed by the Council nowadays.