It's possible you can have criminal charges filed against you, but unlikely if you comply with paying the fine. However, to be safe, it's better that you contact an attorney to discuss the facts of your case in greater detail. Best of luck!
It will be in your best interest to contact a criminal defense attorney. Even if you pay, you may face criminal charges for petty theft. If they contact the police regarding the incident, the officer will submit his report to the prosecutor's office and it will be up to the prosecutor's office whether or not to file charges.
The fact that I have answered this question does not establish an attorney client relationship between the questioner and myself or my office.
It is unlikely that there will be any criminal case if the police never came to the scene. It is equally unlikely that if you pay the civil demand, the store will notify the prosecutor or police of this and no criminal case will be filed. I would also not pay the civil demand without the assistance of an attorney to draft a cover letter that specifies exactly what the loss prevention officer promised and stating that payment is therefore tendered under Penal Code section 1377 and 1378 as the officer promised, if you really want to pay at all.
Even though the amount seems to be small, most likely a criminal case will be filed against you because it is a fairly high number for petty theft. You will need a criminal defense attorney if a case is filed against you. There could potentially be good ending with an attorney on board.
It's not a civil "fine" - it's a civil demand letter. California law allows a merchant to demand up to $500 following a theft incident. These letters are typically sent by the store or a law firm acting on their behalf. They are all bark and no bite. If you ignore the letter, they have to make a choice - let it go or file a small claims case against you. I have never heard of anyone actually being sued if they ignore the letter. Why don't they do anything? Because lawyers cannot get involved in small claims cases and it isn't worth the store's time to pursue a small claims case over such a minor amount. There is one law firm in Florida that does nothing but these kind of civil demand letters on behalf of stores. They were quoted in a Wall Street Journal article as sending out over one and a half million letters a year, but they filed less than 10 lawsuits. Not ten percent. Not ten thousand. Ten. The odds are overwhelming that they won't do anything. If you choose to pay their demand, it just means they won't sue you, but it will have no impact on any criminal prosecution. Paying it won't stop criminal charges from being filed and not paying it won't make a criminal case worse or cause charges to be filed if they weren't going to be in the first place.
You can speak with a local criminal defense attorney for additional guidance about other local issues (for example some counties are seeing police reports and criminal charges even if police were not called initially).
The above answer is for general information only and is based on the information you posted. Every case is fact dependent, so to get a thorough analysis of your situation, you will need to consult face to face with an attorney licensed to practice in the jurisdiction where the incident took place. Do not conclusively rely on any information posted online when deciding what to do about your case.
I don't know if it won't turn into a criminal case. What you don't want obviously is a conviction on your record. So, you will need to fight this with. Speak with a local attorney.