Fishing is best when they are generating, but they don't generate much. They open the spillways when there are heavy rains throughout the year but the spillways by themselves usually don't coax the bigger rockfish up from the Cumberland. You can see the generation schedule and water depth for each dam at the TVA website.
https://www.tva.gov/Environment/Lake-Levels/J-Percy-Priest
They'll start drawing the lake down later in the fall for the winter and fishing will be good then. During the spring rains the fishing is good. During the summer months it's rare to have enough water to fish in. There are weeds 3 feet tall below the dam during a lot of the summer and you can walk right across the Stones river.
Check the TVA site for the generation schedule when there are heavy rains forecast. The big fish come up when the water is at 394 ft or higher (the bottom on the tailwater side is about 388 ft above sea level so 394 ft means the water is about 6 ft deep). The discharge rate is also listed. Fishing will be best when it's high, 3,000 cubic ft per second or more. And it's always better if they are running 1 of the generators. They rarely run both.
Anytime you drive by and there is enough water to whitecap and churn you have a chance to catch them. I have better luck on the Nashville side because the 2 generators are on that side but a lot of people fish the Hermitage side too.
Be careful if you go down there. When the water level is rising and falling those rocks get slick. The brace I'm wearing in the earlier pic is from a torn meniscus and broken knee I got slipping on one of those slick rocks while fighting a big striper. I did get up and land him though
Good luck!