Based on my data, I have external regulatory requirements like PCI, HIPAA, or CPHS. Does an ASTP assessment cover me for those requirements?

No. ASTP assessments only measure compliance with campus minimum application security requirements. Though, it should be noted that achieving compliance with campus standards will lay a lot of ground work for meeting PCI, HIPAA, CPHS, or other external standards. The campus Minimum Security Standards for Electronic Information (MSSEI) is based off the SANS Top 20 Critical Controls, so there is some overlap with external standards.