Are these two annotations related in any way? I'm really not familiar with @JSonAlias but after a quick web search it appears to be a way of using different names for attributes when deserialising JSON data.
@JsonAlias annotation (since version 2.9) can be used to define one or more alternative names for a property which should be mapped during deserialisation.
In spring the @Profile annotation is used within Java configuration to include [inject] POJO's for different configuration(s) in order to facilitate testing. Typically you would have different sets of configuration for different environments. Typically this could be for development, integration testing, UAT/OAT, and live environments.
Not really sure what technology you are using "multiple incoming response"? Would it not be better to just deal with each type of request/response individually, putting common business logic into small reusable POJO's?