Simi Valley is an incorporated city in Ventura County, incorporated on 10 October 1969, and permits inside city limits run through the City of Simi Valley Building & Safety Division, not through LADBS. The City's own FAQ states that re-roofing of more than 10 percent of the total square footage of the roof, or over 100 square feet, requires a permit. A job can therefore need a City permit without triggering other code thresholds, and the permit route, the fee line and the inspection outcome are confirmed at application, not assumed from another city's rules.
For a single-family re-roof in CEC Climate Zone 9, the Title 24 Part 6 prescriptive cool-roof values are an aged solar reflectance of at least 0.20 with thermal emittance of at least 0.75, or an SRI of at least 16, on steep slopes of 2:12 or more, and at least 0.63 with emittance of at least 0.75, or an SRI of at least 75, on low slopes under 2:12. That requirement is triggered when more than 50 percent of the roof area is replaced, which is a different threshold from the City permit trigger, and the parcel's zone should be checked with the CEC zone finder before a product is specified.
The underlayment is the roof's real waterproofing. Shingles just shed most of the water.