No, she is not. This might have been hard to understand in the original post since the screenshots are technically out of order, but the Kimono Girls are supposed give the quest reward, not a Nurse Joy. However, if you happen to reach the Glaceon fight, you will get to progress to the Sylveon fight regardless if you win or lose.
In fact, it is probably better to lose because of this. You get "respawn" at the PokeCenter and now your entire team is fully healed, despite having been knocked out by the previous five fights. If you win against the Glaceon, you'll stay in Route 9 and continue fighting the Sylveon with your knocked out team. Essentially, losing against Glaceon specifically lets you collect the reward from the PokeCenter despite being only partway through the challenge.
This happens only on the Glaceon fight. If you lose versus any other Kimono Girl's Eeveelution(Flareon, Vaporeon, etc.) you won't progress through the fight.
What you're seeing is the images of me receiving the Eevee reward from beating the Kimono Girls despite clearly having lost and being sent back to the Pokemon Center
Edit: Fixed for clarity
Edit 2: I don't think anyone ran into this issue before. I gave a quick search and didn't see anything about the Glaceon Kimono Girl fight. I found one encounter here: https://www.rebornevo.com/forums/topic/49584-majorfatal-bugs-v12/?do=findComment&comment=926391