What are all the games where you can catch a Pokémon while it’s using moves like dig?

Question

I saw this guy catching a shiny dugtrio and it used dig and the ball still hit while he was underground. This was in Gen 2 and now I’m curious when this was changed.

the video in question (around 6 minutes in)

Answer 1

Generation I
...
Pokémon can be caught in the semi-invulnerable turn.

Generation IV onward
Pokémon cannot be caught in the semi-invulnerable turn.

So they can be caught while using Dig, Fly, Dive, ect. in Generations 1, 2, and 3.

Source: Bulbapedia