Are there any adjustments? How is the float attached to the pump? Can you post a picture of the pump?
The pump should turn on before any of the drain pipes emptying into the sump well, as seen in the sides of hte sump well, are significantly submerged.
The good conscientious technician or serviceperson will carry extra oils and lubricants in case the new pump did not come with oil or the oil was accidentally spilled, so the service call can be completed without an extra visit.