Am I being rude to a customer who reached out on my socials?

I’m a 25F bartender, and a customer somehow found my Instagram even though I never gave him my last name or any of my social media. He DM’d me saying he’d “finally tracked me down” so he could ask me out. I politely turned him down and told him that what made me uncomfortable wasn’t him asking, it was that he found my personal account after only knowing me from work. I figured that would be the end of it.

This weekend I was out with friends at a completely different bar on my night off, and I ended up running into him. He came over to say hi, which was fine at first, but then he brought up the DM and asked if I still thought it was “creepy” that he found me online. He said he was just trying to shoot his shot and that everyone looks people up on social media now. I told him I still wasn’t interested, but after that the whole conversation felt awkward, so my friends and I moved to another part of the bar.

Now I’m second-guessing myself. I don’t know if I should’ve just changed the subject instead of answering him honestly, but it felt weird having to defend why I was uncomfortable in the first place. Has anyone else in hospitality dealt with something like this? Would you have handled it differently?