I assume that you are referring to make-up air (MUA) which is needed to replace the air that you want the cooktop hood to remove. Most municipalities incorporate codes that require MUA when the blower's rated flow rate above 400 CFM (actual flow likely to be only 2/3 that). This is to protect against back-drafting combustion appliances such as hot water heaters, furnaces, and dryers. I don't know Alabama state code.

You need to specify what combustion appliances you might have, and where they are located relative to air connections to the kitchen. This will affect the complexity of the MUA system.

I am unclear where your contractor intends to cut the second 10-inch hole. On the outside it needs to not entrain exhaust air from the hood system or any combustion appliance. On the inside its ducting needs to deliver air to the kitchen in a way that minimizes turbulence at the cooktop. The MUA system may or may not require a blower of its own (see ¶2).

Disaster ahead if you do not get the HVAC person involved in the MUA right now.