Is it normal to have a headhunter reach out if you're an undergrad for FT? Asking for references beforehand?

I'm not necessarily set on IB or any particular industry. Had a headhunter reach out regarding a potential "finance" role. They are asking for some professional references which I definitely do have, but aren't these references typically contacted farther into an interview process or more likely when making the candidate an offer? Not sure if I want to have my references called for a role so early or one that I'm not exactly sure what it is since my references will likely have to be contacted again for other roles I'm in the process for.

Am I maybe just overthinking this in that it's actually typical for someone's references to be called many times throughout the course of a few months when looking for a FT role? Anyone have any experience with this? Thank you so much!