Yeah, you were correct. The effect of Perish Song (i.e - The countdown) is placed on the pokemon that hears the song, and will stay frozen if it's switched out by the normal means. Baton Pass will also pass the countdown to the next pokemon you choose, which can essentially mean instant fainting if the countdown was at 1 before using Baton Pass.
Current PC Build
CPU - i7 8700K 3.7 GHz (4.7 GHz turbo) 6 cores OC'd to 5.2 GHz with Watercooling (Hydro Series H110i) | MB - Gigabyte Z370 HD3P ATX | Gigabyte GTX 1080ti Gaming OC BLACK 11G (1657 MHz Boost Core / 11010 MHz Memory) | RAM - Corsair DIMM 32GB DDR4, 2400 MHz | PSU - Corsair CX650M (80+ Bronze) 650W | Audio - Asus Essence STX II 7.1 | Monitor - Samsung U28E590D 4K UHD, Freesync, 1 ms, 60 Hz, 28"
