From the wording of the message, it's almost certainly something in the SSIS package. SQL Agent just runs the package, any "alert" or error condition is created by the package itself, unless SQL Agent cannot run it at all.
I didn't mean to suggest that there was a script task in the package, only that the "time limit" you mentioned was not a built-in feature of either SQL Agent or SSIS. Again, I think the error is actually the presence of rows in the EXC_PRODStaging table.
I'm not an SSIS expert, can only suggest:
Run the SSIS package manually (not via SQL Agent) and step through the workflow in debug mode. Pay particular attention to:
Look in the workflow for the EXC_PRODStaging table, check all the input and output flows for that table. Also check for stored procedure names, and then check the code of those stored procedures to see if they access that table. The logic that generates the error may be encapsulated in the procedure and not the SSIS package.
Search the package contents for the text of the error message "ETL Exception data rows exist". Depending on how you edit the package, there should be an option to "view definition" or something similar where you can view the XML of the .DTSX file. If that's not available, you can open the .DTSX in NotePad or NotePad++ and view the XML directly, then use the search feature of the editor. Do not have the package open in 2 programs at the same time, and do not make or save changes in NotePad.