Their resistance will, and damage sent to henchmen is before your resistance. This is why defence based builds for solid MMs are better than resistance ones, with resistance being just as useful as defence on the henchmen (of course still at 1def=2res) because if the MM doesn't get hit at all, then neither will the henchmen, but they are still there for when a hit happens.
You got it backwards.
The MMs resistance is applied before the damage split, henchmen resistances have no effect on the shared damage.
No, I don't have it backwards. The damage is split, and then the resistances of the individual entities apply.
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No, I don't have it backwards. The damage is split, and then the resistances of the individual entities apply.
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You SURE about that? 
For the record, Shadow Fall on this character is 23.54% Energy Resistance. I tested the effect of it on Damage received by my Tier 1 Bots three times:
1. Completely unbuffed
2. Bots inside Shadowfall's radius
3. Bots outside of Shadowfall's radius (using Defensive GOTO)
Conclusion: the Bots own resistances doesn't matter. YOUR resistances get applied when you are hit, this reduced damage then gets divided as same-typed but "unresistable" damage between your pets.
Couple of questions...
If my henchmen are in bodyguard mode and I get hit with an attack, when the damage gets spread out to my henchmen does their resistance (if they have some to the damage type of the attack) get applied to the damage they will receive?
Similarly if I myself have some resistance, is the damage shared out to my henchmen based the amount of damage before or after that resistance is applied?