Dark Soul: Misery gives you 30% Haste. This Haste means your DoTs tick quicker, and they tick more over the duration, leading to more damage. If you cast a DoT during Dark Soul, it will keep that extra duration/tick speed/total ticks until the DoT is complete. DoTs will always snapshot whatever buffs you have on you at the time of cast, whether it be Haste, or Mastery, or Spellpower, or anything.
To 'extend' your procs, what you do is you extend your DoTs right before your procs run out. Here's an example - you cast Dark Soul, and then Agony - it lasts 24 seconds. When your Dark Soul runs out, your Agony has 4 seconds left on it, and you've gotten 24 seconds of Agony affected by Dark Soul by the end. If you refresh Agony right before Dark Soul ends, however, your Agony has 48 seconds of Dark Soul's effect.
You should try to do this with pretty much every single major buff - Dark Soul, Bloodlust, DMC, PvP trinket, Flashfrozen trinket, etc. Bonus points if you extend your DoTs with multiple buffs on you.
Your DoTs are weak because you don't do this. Because they're weak, your MG looks relatively stronger.
The rest of the gap between your performance and sim is probably due in large part to buffs - no Bloodlust, no Crit, no Spell Haste, no Stats, as well as pots and flask.