Regarding the car, they indicated that the Elantra had been seen in the vicinity, which I’ve assumed meant that it came from a tip, which they then matched up with cameras. Possible the car has some distinctive damage or a feature that they didn’t describe, but makes it visible to investigators.
My further supposition is that the Elantra at this point is circumstantial. There are multiple reports that they used DNA genealogy to find him…which might mean they had his name first, and then matched him up with his car, his residence, etc.
My last comment is that with the information available at the moment there’s no way to conclusively answer how they directly arrived at him, his car, and his arrest/charges. There’s no doubt that MPD, ISP, and FBI have a ton of information that has not been made public. Some of it (tip of the iceberg) will come out once he gets back to Idaho and the probable cause documents are unsealed. That’s going to be just enough to justify the arrest. Anything else will wait for trial, if there is one.
Really, I’d just about bet that this doesn’t go to trial. I’m assuming that there’s a mountain of evidence, little doubt, and very little likelihood of a sympathetic jury. His attorneys will get halfway through discovery and just tell him that if he wants to keep breathing he needs to plead guilty.