Yes and no. As I eluded to in the comments, this takes effect only with "electrocute" Damage Over Time effects. Whether or not they're a result of your skills or guns doesn't matter, it just has to be electric DOT caused by you (deathtrap counts as you).
How it really works is every time an enemy takes electrocute Damage Over Time, there's a chance they'll catch fire, too. It never seems to start upon the initial hit with a Shock attack, and it can happen if you stop shooting but let the enemy fry for a second. Most of Gaige's electrical skills will induce Damage Over Time, so many of them have a chance to burn as well.
In playthrough 1, outside of the DLC, there's no such thing as scaling. Enemy levels are determined solely by the area they're in and your mission (certain missions effectively "level up" areas, notably Sanctuary and The Dust). You can easily check the level of an area by checking out the vending machines in the area, they sell items scaled to the level.
DLC in playthrough 1 scales to your level...ish. It maxes out at level 30. I played the DLC as a level 34 character and was disappointed to see everything was at level 30 in playthrough 1. Not sure if it has a minimum level it scales to.
Playthrough 2 works the same way until you beat the Final Boss; then everything in that playthrough scales to your level (except mission rewards for missions picked up before the final boss).
Playthrough 3 works the same was as Playthrough 2 after the final boss: Everything scales to your level, period. In team play, it will always be scaled to the highest level player's level. And you have to be at least level 50 to unlock it, so enemies are effectively level 50-61 at all times. Though if you take a mission before leveling up, the mission will still stay at that lower level, as always.
Basically the game works like a standard RPG without level scaling until you A) beat the game twice (because you should be maxed out anyway) or B) enter a DLC (because you can do that at any time so a preset level would be a really bad idea)
Best Answer
Green gives you very fast ammo regen.
Yellow gives you large amounts of speed.
Blue Defense gives shield regeneration.
Red Defense gives health regen.
Melee gives massive knockback to all of your melee attacks and increases melee damage.
Damage simply makes you do more damage.