Offering a suggestion as to why he has that spike, whereas you do not.
IF he is tracking his ICDs, which any afflock should be, he may have planned his execute phase DS:M around them - that's what I'd have done.
Details of the spike:
<20% life, i.e.execute phase.
Used DS:M. Planned.
Used Synapse Springs during DS:M. Probably planned.
Kept full haunt uptime during DS:M. Planned.
Near full Drain Soul uptime during DS:M. Planned.
Near full Jade Spirit uptime during DS:M. Sheer luck, the bastard, though he may have noted the initial proc and used his DS:M on purpose then.
Blessing of the Celestials trinket proc during DS:M. Probably planned.
In comparison to your execute phase uptimes, your haunt is patchier, and most of your procs aren't particularly aligned. You didn't have the best uptime on haunt during your DS:M either.
In summary, he probably had a little better luck in tersm of his timings going into that phase, but it's nothing you cant match with a bit of forethought and planning. Stacking buffs/CDs within execute phase is the way to go