Until you have uploaded a mapping from HarmoSearch schema to your local schema, it is not possible to receive data in your own format. The publisher can at most send you data bypassing any mapping step.
The mapping for receiving data pushed by other HarmoSearch participants is the same as the one for receiving import results (see configure mappings for import). For each subdomain (events, accommodations, ...) you can specify which mapping to use within the 'Exchange Data Service' page. If you have uploaded several versions of a mapping, you can set which one shall be used by setting the associated collection identifier.