What varies first is things like the system voltage and spinning loads (like grid-tied motors) and frequency. Then high-speed relays kick in and other things start coming in. This is at the sub-second level. After that, things start to happen at the seconds level and a lot of generation can react that quickly. Other generation takes minutes. The problem is controlling the oscillation as relays, loads, and generation react and trying to limit the range of cascading failures.
In a simplistic view, with a massive load addition, frequency relays will dump loads on parts of the system and the A/C systems on the rest of the system will be left to start up.