If a family applies for an immigration approval using an I-800A they will remain under the guidelines in place by the respective foreign government at the time they submitted their original dossier. See the following noted from USCIS:
• NBC will NOT be assessing whether or not a family meets the requirements of the sending country; only the requirements of the US. For example, singles that met the deadline in China may have to eventually file an I-800A application and meet all of the new Hague standards, but NBC will not deny a the applicant based on China’s new criteria. Thus far, China has indicated a willingness to process all applicants who met the deadline, regardless of whether they have to file a future I-800A. The ASP’s Hague-complaint home study would then contain a statement that the applicant met the criteria established by the sending country at the time of the original application and home study.
Please rest assured that regardless of the type of immigration approval a family is issued, they will be reviewed under the guidelines in place at the time they submitted their dossier under.