As many citations as possible or just a few with fresh content?

A few citations at a time, many are fine but not all at once is the way to go.

OP, it seems like you're using directory, citation, and aggregator interchangeably but each of these are different.

You need to act like a local business, and a local business should list themselves with as many quality local directories as possible, including new ones that crop up, because the customers in that area who use the directory look for service providers there.

If the site is a crappy spammy looking site that a real business owner would not get caught dead listing there, skip that one..

I think your SEO guy is blowin smoke up your ass, or he is using a PBN with NAP and calling it citations.

Although, to be fair, there are some niches you can rank with little more than onpage SEO. I have a client in education that went straight to the top of Houston, San Antonio, Dallas/Ft Worth, and Austin with just onpage SEO and Google Maps listings in those cities.

I have multiple clients sitting in "A" position as we speak.
I have to agree with techxan, Quality over quantity. Only add about 20 citations a month. Most local businesses aren't even doing this. Google compares your ranking efforts to your competitors. If you out of no where just listed 100 citations when all your competitors are only listing in around 70 directories and have made themselves a name the past few years... If you were Google and had access to the most information in the world.. Do you think it would be very hard to notice the difference?