Smashing Spin is a move card, not an attack. And Spiked Mail says: "If this Armor prevents damage from a Melee Attack, the attacker takes 2 Piercing damage." But this happened: I think the spin should not trigger the extra damage, or the word "Attack" should be removed from the armor. Same goes for Barbed Platemail (haven't tested this one yet). Later on, I was fighting some security robots, and thought it would be great to use the spin to get out of their LoS. And I discovered that enemies affected by Smashing Spin turn to face where you end the move, not where you start it. Which was not what I expected, since the damage happens before you select a destination.
They should work the same. Both now trigger on damage types rather than an attack card being played, which is why characters can take extra damage if they draw Ouch! while either armor is in hand. As Robauke pointed out, the same thing happens with other moves. The "turn to face attacker" coding appears to execute at the end of the move rather than the point of interaction. The latter makes more sense to me, but at least the execution seems to be consistent.