If this is a warm standby config, with ASE1.DB1 the primary/active database, and ASE2.DB2 the replicate/standby database, and assuming the table 't1' is in sync prior to performing your dual inserts, then:
re: the DSI into ASE1.DB1
- should stay up
- should be dormant/inactive while transactions are flowing from ASE1.DB1 to ASE2.DB2
- would become active if/when you issue a 'switch active' command thus causing transactions to flow from ASE2.DB2 to ASE1.DB1
re: the DSI into ASE2.DB2
- I would expect the first insert to be applied successfully by the DSI into the ASE2.DB2..t1 table
- I would expect the failed/second insert to not generate a replicable transaction, ie, the ASE1.DB1 repagent won't send anything to the repserver so there'll be nothing for the DSI (into ASE2.DB2) to do (ie, said DSI will stay up)
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Have you tried testing your scenario to see what happens? ("When in doubt, try it out!")
If you have tested your scenario ... are you seeing a different behavior than what I've outlined? If so, what are you seeing (to include complete text of any error messages)?