Quite correct.
I wish the vaunted travel bloggers and other online luminaries would hyper-actively promulgate this nuance, before people deliberately put charges on their cards before their December closing date mistakenly thinking they'll be credited.
Except it changed in May 2017 or so. For cards opened since then, the credit is based on the cardmember year, so a card opened in September 2017 won't get the second credit until September 2018. For cards opened before the change it's still based on the calendar year.