not sure about lancers, but with listers minions they won't apply amp, ever. Might be similar with champ minions, and if so, you will need either an elite or a trash unit, not an in between.
Its my understanding that bound minions display their affixes but they don't work. Haven't tested all of them, perhaps they get the added lesser elemental damage from enchantments, but they don't get any functional cursed or enchantment resist or so on
Because that's how minions work in general, they display the affixes of their unique but only get partial / no bonus
do Tainteds also snapshot the Demonic Mastery lvl when you summon them or only Tainted skill lvl?
I mean its been a pretty safe assumption so far but I don't think anyone's actually tested it- it should almost certainly snapshot at cast
It makes sense given how blizzard coded these minions to look up your skill levels when cast to set their parameters, and would be a real surprise if it used current value. Easiest test would be get a ~100 damage tainted, equip +99 mastery for +990% damage and see if it deals 11x the damage now
Its also why mang songs is better than a +3 demon / +3 tainted dagger, which could be shopped but would be extremely hard to shop. Its +131.25 damage / +50%, vs +157.5 damage / +30%