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 average homeowner who lost his house in the Oklahoma tornadoes should move for good and not rebuild. Too much complexity watchdogging the contractor. Too much a chance to be defrauded.