Legal Question in Criminal Law in California

It's against the law for private employers in California to ask employees about arrests that don't lead to convictions. (Lab. Code, sect. 432.7.) They can only asks about actual convictions.

"any record" means conviction. You haven't.

Was the question written exactly as you have stated it? If so, it's quite odd. The question does not seem to ask specifically about criminal records. After all, "financial irresponsibility" isn't a crime. Neither is alcohol abuse, though such abuse sometimes leads to criminal behavior. The same is sometimes true of substance abuse, since there are substances which can be abused even though owning them and using them is legal.

At best it is unclear whether the question is asking if you've ever committed domestic violence or if you've ever been convicted of it.

And since it sounds like you already have your new job, the question evidently was not part of your job application. Mr. Roach describes some of the rules that applications must satisfy, but if this question comes from a different kind of document then it may not be subject to those rules. Besides, the rule that forbids employers to ask about arrests might not apply to questions that ask only about your conduct and not whether you were ever arrested for it.

You should probably invest in a couple of hours of a lawyer's time to discuss your situation in more detail.

Good luck.