How does a disputed charge go about with Amex, will the merchant bill me directly?

I just recently got some auto work completed about two weeks ago and two weeks later the problem that I had worked on at this particular auto shop arose again in exactly the same way as it was before I brought my car into the shop. I called two days ago to let them know I would be coming in because the problem was not fixed as I thought it would have been. I brought my car in this morning and one of the mechanics spoke to me and tried to charge me for more diagnostic fees which the manager on the phone said I would not have been charged since they didn’t fix it properly. The guy tried to charge me and then tell me I had to wait a few hours, I felt like I shouldn’t have had to wait a few hours since it should have been completed the first time around! I was willing to wait though.

I also told the guy that I talked to the manager and the manager assured me I wouldn’t have to wait since this was a “come back” repair. So when I brought this up to the guy, he immediately was willing to take my car back. I told him I wasn’t going to pay any diagnostic fee since it wasn’t my fault the same problem arose. I told him that for two weeks, it felt like the problem was fixed but low and behold same exact problem came back.

When they finally looked at my car, they were being really rude and disrespectful with me, especially since I am just a 23 year old girl who came alone and know nothing about cars.

The guy tried to tell me that my spark plugs needed replacing, but i told him that they had already charged me for a new set of ignition wires and spark plugs! Then they tried to tell me that I never told them about this issue before and that they are not going to redo the work for me without me paying again since I didn’t tell them about this problem the first time I came in. This part is a lie otherwise they wouldn’t have gotten me to pay for the work done on the ignition if I didn’t tell them something was wrong with my starter! They basically told me they couldn’t help me at the moment and that I needed to come back another day. They didn’t really seem like they believed me and wouldn’t help me fix the problem I had paid to be fixed.

Anyways long story short, the guy belittled me, made me feel extremely uncomfortable by the way he was talking to me and disrespected me and tried to scam me into parts/services that I shouldn’t have had to pay for….again. Since the work was not properly completed I called up Amex and disputed the charge and told them about the customer service and the time I wasted being run around and being belittled and made feel extremely uncomfortable.

Amex told me that they would put do a “courtesy credit” to my account until the investigation is over. I am wondering, if the courtesy credit becomes permanent, and Amex disputes this with the merchant with me, will I be billed by the auto shop later when they didn’t receive my money from Amex?

I just do not want to see, hear, or talk to the people from this auto shop again, this was just not an experience I want to go through again. I just want my money back so I can get this problem fixed at a better auto shop and get it repaired properly. I am just scared that they are going to try to contact me since they have my address and phone number and try to bill me directly for the charges if Amex refuses them my money. I just don’t want to take this car somewhere else and get it fixed, pay the bill for that and then be slapped with the bill from the first auto shop who Amex wouldn’t pay.

I asked the customer service rep at Amex if the auto shop would be contacting me because I told her I am frightened by them calling me up because they know my number and address. She told me that once this dispute has been opened, it is between Amex and the merchant and they will not be contacting me. But I am scared that afterwards the merchant will try to contact me and force me to pay them for the non-repair repair work they did.

Please give me some insight as to what happens after a dispute is settled. Will the merchant come directly to me for the bill even if Amex rules in my favor? And what do I do if they do that?

Thanks in advance!
Thank you Colorado Papa for responding to my question! I appreciate your help.