"We are tier 2 customer, we supply to automotive but not OEM. How does customer specified requirements fit in?"
Customer specific requirements are only those required by your customer, in this case the Tier I.
"This in regard to ISO/TS 16949 registeration"
You are required to demonstrate compliance to all clauses of TS2, including customer specific requirements "flowed down" by your customer.
"Do we need to submit our customer requirements based on the supplier requirements manuals they submitted to us?"
Check with your customer.
"Would we be audited on those defined requirements?"
You will be audited for compliance to customer specific requirements