It sounds like the account that runs it as a job (the sql agent service account) does not have permission to access the MyServer MyDB database.

You need to give it permissions to read the data and also windows permissions to any folders and files accessed in the package such as access db or excel sheets or flat files.

When you personally run the package from the data tools - what you call SSIS, it uses your account credentials so you have permission and the package runs.

It is also usual to give the agent account db_ssisadmin permission to msdb in the user mapping section.