No, this does not necessarily mean that your case will be denied automatically, however unfortunately it is a possibility.
The immigration supervisor will be reviewing your case to make sure that you have "good moral character."
Has it been 5 years since this conviction took place? If so, that is something USCIS considers, and it works in your favor for a finding of good moral character. If it's been less than 5 years, then it is possible they could view this prejudicially and deny your petition based on a finding that you lack "good moral character." Hopefully this doesn't happen, but it is possible.
Also, the way immigration deportation laws work is that if you commit a "crime of moral turpitude" that is punishable by one year or more in jail, within 5 years of having been in the US, it makes you deportable. If this was a misdemeanor though, punishable by less than one year in jail, then this should not be applicable to you. But it does go to show that USCIS looks at domestic violence crimes rather unfavorably.
Again, making a finding of "good moral character" is why the person you interviewed with needed to take your case back to a supervisor for review. Hopefully you'll still be able to naturalize, but again, depending on the facts of that underlying case, you may be denied at this time.
If that does happen, then you will want to wait until it has been 5 years since the date of that conviction, before you try to re-apply for naturalization. My recommendation would be to hire an immigration attorney to help you with that as well, and ensure that everything is filed correctly next time.
I hope that helps! Please let me know if you have any other questions. Also, please take a moment to kindly rate me using 3 stars or more, as this is the only way experts are compensated for our time here on 'just answer'. I do not receive a salary here, and am only compensated for my time after you leave me a positive rating. The question won't close after you rate me, so you can still ask any follow-up questions you might have. Thanks so much, I appreciate it!