No they shouldn't have billed you for a new month. I haven't had that problem. I know they don't like to give money back. I wish I could help out, but I haven't been in your situation. It cancels for me when I cancel.
Qobuz hell
Ending a subscription with qobuz turned out to be hell. I did it two weeks ago only to find out that my account is still active and I am still being charged. I contacted qobuz yesterday and the first response was from a bot saying at 9AM they will be back online tomorrow. Which is actually today, so when I got online to figure out what happened, I received the rudest, most useless responses and then ending the chat by the agent. So as of now, I am unable to cancel my subscription - I don't want to use it, pay for it etc. I found it mediocre anyway.
I have no doubt I will spend many hours trying to cancel it in the coming days and get horrible treatment.