Your understanding is good for Gen 3 but not Gen 4.
In Gen 3, the frame (as in: the RNG frame, defined here) advances each time the game draws a new frame (as in: the picture that refreshes at 60 Hz) to the screen.
You can use an RNG tool to see that this does indeed lead to shiny frames being generated every few minutes on average (and often in big clumps due to the simplicity of the PRNG used), but it's important to note that your odds are still bound by the 1/8192 probability, not the rate at which the frame is turned over.
In Gen 4, frame advances aren't tied to the refresh rate and instead occur at the particular times the game needs to create a random event. That event could be something like generating the stats of your wild encounter, or something as simple as which direction an NPC randomly turns next. More examples relevant to RNG manip are listed here.
For Gen 4 RNG manip, it's also worth noting that the game tracks multiple RNG states that are advanced through different means and used for different purposes (e.g. PID generation versus IV generation).