SSIS comparison load between new, updated and deleted records and populate a staging database
If I've understood correctly your OLE DB Destination is to the 'target' table and your OLE DB Destination 1 is to the 'staging' table? That would explain why your new rows aren't appearing in the 'staging' table as you're only sending them to the 'target' table.

If you want all rows (updated or inserted) to appear in the 'staging' table, I would suggest you remove the Lookup and Conditional Split and simply insert all rows to the 'staging' table. Then use a Execute SQL task to fire a MERGE statement to update or insert as appropriate to the 'target' table. In my experience this is much more performant that using the lookup to decide whether to insert or update