Whenever INSERT is happened in the CUSTOMER table,I need to call the \"StoredProcedure1\"and UPDATE is happend in the CUSTOMER table,I need to call the \"
Let SQL Server be SQL Server, and have it do the work for you!
Create separate triggers for each change event (insert,update and/or delete). Put the logic for each into the trigger that needs it. No need to have to check for the event type.
And don't call a procedure unless it is quick, fast, and can't block others.