I strongly suggest you check with the local building department or electrical inspector before you let this electrician do any work.
The subpanel is not a separate electrical source since it is in the same building as the service. Therefore it must be grounded at the point of the electrical source which is your main panel. Regardless if you put a separate ground rod for the subpanel, you MUST ground that subpanel back at the main panel. You cannot ground anything upstream of the main circuit breaker on its own ground. In other words, add all the ground rods you want, but you still need to ground back to the main panel.
What I suggest, and what I did in my house (which I do not want to burn down), is to install a 2-pole breaker in the main panel. Run wires from this breaker to your subpanel (no main breaker required in the subpanel). Run a separate neutral from the main panel neutral bus to the neutral bus of the subpanel. In the subpanel, install a separate ground bus. This ground bus MUST NOT be bonded to the subpanel or the subpanel neutral. Run a separate ground wire from the subpanel ground bus all the way back to the main panel and join it to the ground at that point. Connect your dedicated circuit grounds to the subpanel ground bus and the dedicated neutrals to the subpanel neutral. This is effective and legal.
You cannot ground seperately, unless your jurisdiction permits it. The reason for the ground is to trip circuit breakers, as the ground becomes an "escape hatch" for short circuit current in the event of a fault. By using separate or multiple grounds, the possibility exists that a short circuit may be routed away from the breaker, causing a dangerous situation.
