The reason Lunatone was able to use Hypnosis after the "one turn" of Taunt is because in Gen 3, the first turn of Taunt is the turn you use Taunt. Take a look at these Gen 3 OU replays:
In this one, I purposely gave Mightyena a speed lowering nature so it can use Taunt after Lunatone moved. Lunatone was able to used status moves on Turn 3, as Mightyena was able to use Taunt, since Turn 1 was the first turn of Taunt to take effect.
In this one, Mightyena has more speed than Lunatone so it can use Taunt before Lunatone can use a status move. Mightyena was able to Taunt Lunatone on Turn 3 as Taunt's first turn is the turn you use Taunt.
Remember how in Wolfe's Emerald Nuzlocke video, Lunatone used Calm Mind before Crawdaunt used Taunt? Well, had Crawdaunt been able to move before Lunatone, Taunt could've stopped Lunatone from using Calm Mind. Hope this helps.