Incorrect voltage at light sockets
In residential interior wiring, voltage irregularities generally are only a concern when over-voltages are seen and not under-voltages.  Incidentally however, when there is an under-voltage, there is usually an over-voltage on the opposite phase somewhere else to balance it out.  

113V is fine. Light bulbs, except for the LEDs, are pure resistive loads and will not burn up from under-voltages. Now 130V would be a problem if the bulb is not rated for 130V.

I would also consider hiring a different electrician as what he suggested is nonsense.