We are Publishing a JMS message (which contains a unique id) on a Queue (in the beginning)
So it sounds like your unique ID is in the message payload.
The flow goes through multiple Adapters/Databases in between
There will probably be no JMS parameter stored, against which to correlate.
Then we are Subscribing to a Topic (which is in different domain)
Good, so you're getting a copy of every message. It's up to you what you do with that copy (discard it or respond to it).
The problem is it is fetching data/XML corresponding to other unique ids (which are published by other systems/Queues)
That's completely expected. You need a correlation scheme to determine what you discard and what you act upon. There are three correlation schemes. MessageID-to-CorrelationID, CorrelationID and JMS Payload. You say that your unique ID is in the payload, so you want the payload correlation scheme, which I linked to in my previous response.
How best we can manage this scenario where we can fetch only the details of the unique ids sent by us?
You manage the scenario by following the documentation in the link.
We are using CA LISA 7.5
That version of LISA has the JMS Payload correlation scheme built-in.