Government as a Contractor. Subcontracting Requirements?

We recently encountered a situation (albeit a positive one) unique to us and seek information related to the Small Business Subcontracting Program. A state university has an office which provides contract-based courses to commercial entities and will now offer it to government agencies as well. For federal contracting, would this organization be required to comply with the Small Business Subcontracting Program assuming all other factors were in play i.e. size of the task order, issuing agency required a small business plan, etc.

What other information might be helpful in working to a conditional/unconditional response?

Thanks!

TheASBCGuy