Shaco Boxes and TLD/DFT

As a disclaimer, I could be stupid and I could have read over something talking about this already, but I'm curious.

Shaco's boxes don't count towards Thunderlord's Decree even though 1) it's a damaging spell, and 2) it doesn't count as three instances of damage, like Morgana's W does.

On the same token, Deathfire Touch doesn't proc at all, even though Shaco's boxes count as a damaging ability. Whether or not the attacks would count as a DoT or a single target ability would be up for dispute, but I feel like they should be affected by those two in some way.

Again, I could have missed something about this ability in particular, I just found it curious how neither keystone would work with it.