No they are not. They train their models on Adobe Stock content. They do not train on user content.

https://helpx.adobe.com/manage-account/using/machine-learnin...

"The insights obtained through content analysis will not be used to re-create your content or lead to identifying any personal information."

"For Adobe Firefly, the first model is trained on Adobe Stock images, openly licensed content, and public domain content where the copyright has expired."

(I work for Adobe)