Did a website for client, local ISP refers to old hosting name server?

Hello

I have a client for whom we launched a website on June 1st. We switched their hosting from a local company to GoDaddy and saved them a lot of money. I don't know if this issue is the old company messing with us, an oversight with our dns files, or a local ISP issue.

Previously the local company transferred the domain to us in the spring and we left their hosting up until June. The problem is when any customer with the local ISP of our client is getting their old site. (Which is bad because he is a local business)

I called the local hosting company who was very short and rude with me. They said that the website was forwarded correctly and we did everything right.

I called Godaddy and they checked the dns @ and a records and they also said that it was pointed correctly.

I did a traceroute on my clients computer and is showing the local hosting still. I switched to Google dns and it pulled up the new site. I also had one of his customers call me and I put Google dns on her PC and it worked fine.

I thought it was possible a caching issue or his router or PC but he has called me and said he is getting phone calls that the website is down by local customers. I have called the ISP 3 times and they escalated the ticket to tier 3 support but I was wondering if there is anything I am missing here?

Also if there is another subreddit that might have an insight. Not sure if this is the best place but thanks for reading.