For those who haven't done the research and theory-crafting on when you should be using Raging Strikes/Mega-potions of Intellect I'm here to save you the trouble and to improve your damage output:
The way damage over time works in this game it's kind of like a picture being taken: In order for your DoTs to receive the damage increase from RS/potions you MUST use the buffs first. When you apply your DoTs they are applied with the increased effects. So using RS after they have been applied will NOT increase their tick damage because it wasn't an effect present in the initial application.
"But Fester is my hardest hitting move, shouldn't I be saving RS for that?" No. Just no. Your Bio, Bio II, and Miasma deal far more damage than Fester and Ruin spamming. Fester may be the hardest instant hitter but slow and steady wins this race. Also with the correct rotation you can get in 2 RS affected Festers even when applying all 3 of your major (Miasma II is viable also when partnered with Contagion, so long as you're fighting a boss where it isn't dangerous to stand nearby) DoTs anyway.
Raging Strikes>Bio II>Miasma>Bio is how you should always start a fight so long as there isn't going to be a DPS race within the next 3 minutes. Also, it is highly important you try to use RS only when Contagion is going to be available before your DoTs expire, that's an extra 15 seconds of improved DoTs. The same also goes for intellect potions.
Another good thing is "Yes, Bane will spread your RS improved DoTs!" So for example during the first phase of Twintania where there are 4 dragons in total I will target Twin, pop RS and a pot then apply all my DoTs with Contagion and then Bane her to spread them.
Does Raging Strikes effect pet abilities such as Enkindle? Unfortunately no. Enkindle counts as a move used by a separate player and therefore does not benefit from your self-buffs. But Rouse and Spur does increase its damage!
So please my fellow Summoners, use Raging Strikes/pots and then your DoTs.