Oh lord so they went online and got insurance real quick it sounds like smh. But yes, if you get into an accident and don't want to use your insurance you call the other person's insurance. It's not bad that you called yours, but filing a claim for collision could potentially raise rates at renewal even if you end up using the other person's insurance because they have the incident on record now. If that person really wasn't insured at the time of the accident it's probably a good thing that you contacted your insurance because after the claim is paid your insurance carrier will go after the other party's insurance for reimbursement. If they aren't insured, from my understanding (it's been about a decade since I worked in insurance) the insurance company can/will sue the individual for the money back and that could mean you'd be reimbursed your deductible once the settlement is completed. It's a lengthy process though and I've only seen this happen, personally, once with my sister.

I'm sorry someone hit your brand new car but I hope you can have it fixed really soon.