Thanks for letting me know. Sadly I can't reproduce the problem on my end :(
I caught a new Busk and leveled it up to 10 and it evolved after the battle ended.
The evolution should trigger after the battle is over (even when losing). Also the evolution should trigger again after the next battle, because the monster still fulfills the condition (lvl 10) to evolve.
Very strange, that it doesn't work for you. If you have more infos about it, please let me know.