Minion damage related question

Hello, for a few days now I've been testing a spectre based necro build using equilibrium. I understand the mechanics, but its hard for me to figure out if it actually works. I am supposed to trigger equilibrium with fire-based skill and let my Slave Drivers take over with pure electric damage. Yet I notice that they attack with two different beams at the same time, the electric one that slave driver has and a red one. I am thinking if my spectres attack with two different elements at the same time, the equilibrium mechanics do not work as it is supposed to. I looked my items again. The only dark spot I found is that my rare gloves add to my character chaos damage. My question is: If they add this damage to my character, does this damage apply to spectre's skills as well? If yes that would explain the mixed beams in spectres skills. If not what am I missing here? Thank you in advance for your answers

Could your please make the Characters tab of your profile unhidden? This will make helping you a bit easier! You can do this by clicking on your account name (top left corner), clicking Privacy Settings and unticking the 'Hide Characters tab' checkbox.

Elemental Equilibrium (EE) works mostly as you've described. You hit a monster with fire damage and that monster will get +25% fire resistance and -50% lightning and cold resistance. Your spectres' pure lightning hits against the monster then deal significantly more damage without altering the effect of EE, as this effect can only be applied by you.

Damage added specifically to your character is generally not added to your spectres (and vice versa). For example, the added damage from this Murderous Eye Jewel is only applied to your character whereas the added damage from this Ghastly Eye Jewel is only applied to your minions.
In this case, added chaos damage from your gloves will only be applied to you and will not be applied to your spectres. It also will not have any impact on EE, as chaos damage is not elemental damage.

I'm not entirely sure what the red beam you've mentioned is, but a look at your character could help clear things up :)