I agree she is a general first and foremost, in what I believe is her first appearance in the clone wars season 1 episode 13 Jedi Crash; the episode description at the beginning of the episode is:
"When Anakin Skywalker is gravely injured in battle, Jedi General Aayla Secura must teach Ahsoka the Jedi philosophy of having no personal attachments -- while they brave a hostile planet in search of medical help for the Jedi Knight."
But I also did some research on this, and there seems to be some distinguishing attributes for general ranks
- High Jedi Generals & Senior Jedi Generals (Masters such as what we see above + Anakin)
- Jedi Generals (refers to Jedi Knights such as ahsoka, Barris)
- Jedi Commanders (Jedi Padawans)
So technically at the start of the clone wars (SW attack of the clones) she was a Jedi Knight which means she would not have met that greater category
And it is said that after most events in the clone wars she then became a Jedi Master (the larger category) towards the end of the clone wars.
So if they specifically said the high general thing it would be different but otherwise you're 100% right
