It gets 20% of the Warlock's shadow power as healing, I tested this on my own time.
The increase you noticed was your Warlock using a trinket before recasting UA.
It has absolutely nothing to do with the Paladin's spellpower or abilities in any way shape or form, beyond him applying the Judgement (and having t4 2pc, if applicable).
I have some numbers testing from elsewhere, let me get them for you all.
Edit: here's the two posts I made elsewhere, apologies for not re-formatting them.

Well, it's a single entity doing it; everyone in the melee group on the malchezzar WWS from before got healed for the same 308 max and 279 low for "boosted" lights. I have negligible spellpower in damage gear, so it isn't using my spell power for keeping it up. Atta has 708 spell power that affects healing, so if your guy is at 900 the peak of 400 some might have been his 900 + a trinket boost when he applied it. What trinket does he use?
I'm currently checking the actual log file to see which paladin applied the JoL each time for the different values.
Edit: both times it was Talmage. Same Paladin each time. Forad was doing wisdom.
edit:
OK. Starts out healing for 101. This is base 95 * 1.06 (Improved Sanctity Aura), so that's to be expected. That means the 308 peak heals were all really for 290.
UA goes up. SoL heals for 279. With aura effect, that means it is really healing for 263. This is supported later on, It heals for 263 when I have to run out for an enfeeble and the aura fades from people. Later on it drops back to base value and goes back to 279's when UA is reapplied. Same value both times with UA. Edit: and it was 279 AGAIN even after the judgement was redone.
Now let me find what happened when it was healing for 308...
Edit: it was healing for 308 when Atta cast an Unstable Affliction right after proccing Flameshadow from his T4 2pc. Which is +135 spell power. He used no other active trinkets during the fight- at all. If it goes from 263 --> 290 with 135 spell power, that means a 27 point gain while 135 spell power is active, which means exactly a 20% coefficient. So now we need to check, does a 20% coeffcient for shadow damage power fit with other observed results?
Edit again: Atta has 860 shadow power right now under normal conditions. 20% of 860 = 172. 172 + 95 = 267. Doesn't quite fit. However, it's possible he was using a different trinket or slightly different gear during the fight, since he never triggers any trinket during the Malchezzar fight according the the WWS. If he had 20 less spell power four days ago than he did during the last time armory updated earlier tonight, than that would solve the problem and reveal what is going on.
My suspicion is that this is what causes it. Further testing is needed.
Edit again: side note of assuming your dude has 1300 shadow power gives 355 base heals, making that 376 with Sanctity. 400/proc is easily within reach of a trinket and consumable load-out of shadow power boosters. 42 for wizard oil, 65 for shadow power elixir, 150 for a trinket. 1550 * .2 = 310 + 95 = 405.
It all almost fits and I bet proper testing would nail it.
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Just did some proper testing with Blasted Lands immortals; numbers as follows.
Conditions: sanctity aura was off. Healing was baselined to 95. Warlock had all gear and Fel Armor on. I hit the mob, he did nothing but cast UA once each test. (repeated each test ~5 times to confirm numbers)
HIGH POWER: 1018 - 298 heal, occasionally 299.
That means a 203-204 boost.
1018 / 5 = 203.6.
It fits.
Weapon and offhand removed. Fel Armor turned off.
LOW POWER: 736 power - 242/243 heal.
That means a 148 boost.
736 / 5 = 147.2.
It fits.
This is almost certainly how spell power is added to JoL.
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