Now in my case i had a trigger which need to fire each time i instered some data into the table. Actually, i was updating the stock rate and needed to copy the rate by trigger. But to my surprise, the trigger was not firing when i insert/update the data by the SSIS. But the trigger fires when i do the update by SQL.
The problem is with the settings in "OleDB Destination" inside "Data Flow Task". Here is how i solved the issue
Right click on th "OldeDB Destination" and you will find "Show Advanced Editor" and open the Advanced editor.
In the editor check the "FastLoadOptions" which is by default "TABLOCK,CHECK_CONSTRAINTS". You need to add one more option "FIRE_TRIGGERS" . And thats it. But remember the trigger runs once for each update/insert. Not for every update/insert. So in case where we are doing batch update, you must write the trigger code in such a way that it will be able to handle the situation for multiple row sets. Here is a sample statement
CREATE TRIGGER UpdateStockRate
SET CMP = i.LastTradedPrice
FROM INV_tbl_Holding t
JOIN INSERTED i
ON i.Symbol = t.Symbol