How about deleting the reminders programmatically using the event ID that you got after inserting the event?
ContentValues cvEvent = new ContentValues();
cvEvent.put(Events.DTSTART, startMillis);
cvEvent.put(Events.DTEND, endMillis);
cvEvent.put(Events.TITLE, strJobName);
cvEvent.put(Events.CALENDAR_ID, mlCalendarID);
cvEvent.put(Events.EVENT_TIMEZONE, "America/Los_Angeles");
Uri uriEvent = crEvent.insert(Events.CONTENT_URI, cvEvent);
//added code
long eventID = Long.parseLong(uri.getLastPathSegment());
ContentResolver cr = getContentResolver();
cr.delete(Reminders.CONTENT_URI, Reminders.EVENT_ID+"=?", new String[]{eventID+""});