The roofer must understand materials, capillary action, ridge vents and flashings, counter flashings, base flashings, spud bars, rake boards and soffits, shingles and shakes.
In addition to continuous eave vents, you probably need continuous ridge vents, but you can probably get by with doubling the number of roof vents you have now.
The kind of vent at the foreground of their suggestion is chemically more similar to the warm (ca. 100 C) off ridge vents such as Lost City than to the more familiar black smoker type vents (ca. 350 C).
Screen open eaves and soffits beneath the roof and gable and ridge vents at the peak.
But the roof is properly equipped with ridge vents (an overhang between the walls and roof for ventilation and fire-retardation), so we're almost to code.
For top vents, merely having one in the gable at each end may not be enough; roof turbines or ridge vents may also be necessary.
You could use a roof-mounted exhaust fan just as well, but will probably need more than one fan to get as much ventilation as a series of ridge vents would provide.