whenever i'm deleting a page from siteadmin and asset from asset console. it also deleting page/asset from publisher instance but this is not happening when im deleting it from crx. is this normal behavior or i've changed some configuration?
This is normal as via the console, it will do the invalidation via replication as well.
If you are deleting via crx, you need to use the replication tab and replicate the parent node to get the change.
This is correct behavior.
When you delete from console a workflow get triggered internally and first it de-activate the assets from publish and than removes it from the author.
you can see the delete "POST" call in the replication agents.
>> POST /bin/receive HTTP/1.0
>> Action: Delete
From crx/de it is hard deletion and the internal process did not get trigger.