Unfortunately this just keeps getting more complicated ...
From the slew of questions it's not apparent (to me) if a) you've got a valid warm standby configuration for active=ASE1.DB1 and standby=ASE2.DB2, b) you're not familiar with with how warm standby works and/or c) you got warm standby setup and then (possibly) made some configuration changes.
You've provided no actual error messages so it's not apparent (to me) why your DSI is going down.
You've not explicitly confirmed the structure of both tables are in fact identical.
You've not explicitly confirmed both tables contained identical data prior to running your dual inserts.
You're now talking about directly inserting records in the RDB ... which should not be the case in a warm standby setup otherwise you *can* run into all sorts of bad things happening (eg, dup key errors, DSI going down).
At this point I'd suggest you start over from scratch ...
- create new PDB/RDB databases; create identical/empty table 't1' in both databases; create identical unique index on both tables
- create brand new WS setup (create logical connection; rs_init ASE1.DB1 as active db; rs_init ASE2.DB2 as standby)
- verify replication is working by submitting rs_ticket in PDB and verify it comes out in the RDB; once replication if verified then ...
- insert first record into t1 in the PDB and verify it gets inserted to RDB's t1 table
- insert duplicate record into t1 in the PDB and see what happens