Eligibility won't have anything to do with whether you owed or got a refund on taxes last year. It's based on your Adjusted Gross Income (AGI) threshold values. When they say it's "nonrefundable" (confusing word IMO), what they mean is that you can't get a net payment from the government on it (i.e. can not be higher than your "Total Tax Liability").
Simple example: Let's say your AGI was $20k for the year, and that your total tax owed for the year was $3,000. You can't get the entire $7,500 credit because that would make your total tax liability negative (-$4,500). Therefore, they limit the refund to what you owed ($3,000). I have no clue how that all works with a Point-of-Sale system to know what it's limited to. Only one of last/this year needs to qualify, so I expect they might need to have you upload your 1040 for them to check last year's tax filings? If you qualify, you're golden. If you don't, maybe they give a provisional credit? I expect the car dealer is taking the risk at that point.
Again, the April 15th Tax Filing (what you owe, what they refund) is not relevant, it's AGI and total tax liability. Not the "settle up" you do when you submit the 1040 filing.
Hope that helps?