The PROCESSMAKER_OPERATOR role has the PM_CASES permission. An Operator can't see any cases without the PM_CASES permission. Are you thinking of another permission?
How are you executing your trigger? If you are using REST or the executeTrigger() web service, ProcessMaker will check whether the logged-in user is assigned to the task (indicated by the delegation index) in the case.
ProcessMaker doesn't provide a way to pass arguments to a trigger. What you have to do is set variables in the case and then have your trigger code use those case variables. Then you can unset those variables in the case if you don't want them to remain.
If you install the extraRest
plugin, there is a REST endpoint that allows you to set variables, execute the trigger and then unset the variables in one operation.
That endpoint also allows you to get around the security restrictions that are probably causing your problem.