Under the rule, the agency said it would oversee the non-bank auto lenders to ensure they comply with federal consumer financial laws, including the Equal Credit Opportunity Act, the Truth in Lending Act, the Consumer Leasing Act, and the Dodd-Frank Act prohibition on unfair, deceptive, or abusive acts or practices (UDAAP)."We're not sure where they got the number 34, but we're pretty sure that most or all of them are our members," National Automotive Finance Association Executive Director Jack Tracey said.

Tracey added that almost all non-bank auto finance companies belonged to either NAF or the American Financial Services Association, and some had membership in both, he said.

Non-bank auto finance companies include those that lend directly to consumers and those that finance auto loans indirectly, the agency said.

Tracey explained that because the final rule changed very little compared to the originally proposed rule, which the agency issued in September 2014, most of NAF's members have already had the opportunity to adjust to its impact and shift their operations accordingly.

"I think people generally liked that there weren't any big surprises in the rule," Tracey said, adding that his members appreciated receiving a rule rather than having the agency regulate through enforcement actions.

Read more: Enforcement actions catch the industry off-guard …

When the agency regulates through enforcement actions, Tracey contended, the industry is always caught off-guard and left wondering whether or not certain practices are allowed. A rule, by contrast, provides the industry with a solid line in regards to compliance, he said. In addition, the comment period during the rulemaking procedure gives industry members a chance to voice their opinions as the agency writes the rule.

When it announced the rule, the CFPB said it would examine non-bank auto finance companies for their marketing, credit bureau reporting, debt collection and fair lending practices.

The CFPB also said it would assess whether the information auto finance companies provide to credit bureaus is accurate, and pointed out that it had recently taken an enforcement action against an auto finance company that distorted consumer credit records by inaccurately reporting information such as consumers' payment history and delinquency statuses to credit bureaus. The CFPB said it would act to prevent auto finance firms from reporting inaccurate information in the future.

The agency also said it would assess whether or not auto finance companies use illegal debt collection tactics, affirming that it would try to ensure collectors rely on accurate information and use legal processes when collecting on debts. The CFPB said it would review the repossession process, including the practices of third-party service providers that finance firms hire to repossess automobiles.

Tracey said he was unsure of the exact impact the CFPB's regulations would have on the marketplace for two reasons.

First, since many of the non-bank auto finance companies that are likely subject to the new rule primarily utilize indirect lending, their brands may not be widely recognizable to consumers. And, it is unclear whether auto dealerships would care one way or another if they are regulated, he said.

However, Tracey estimated that over time, the CFPB's rule would likely have a positive impact on non-bank auto finance companies' positions in the marketplace.

"After this, everyone will be playing by the same rulebook," Tracey said, noting that this will make it easier for the industry to become and remain competitive.

The National Auto Dealers Association declined to comment on whether the CFPB regulation might make a non-bank auto lender more or less attractive to car dealers, as it is currently involved in a fight with the CFPB over proposed agency guidance that restricts or eliminates the dealership's role in setting interest rates for indirect car deals.