RULES UPDATE: "When (not immediately after) this effect resolves..."

Discord user Shining Blue-Eyes has unearthed mounds of evidence concerning the validity of a 2004 Netrep ruling for "Ultimate Offering":

• "The Summon produced through the effect of "Ultimate Offering" may be negated only if that Summon was the first link of a Chain." [REF]

The Netrep ruling fell out of use and judges were of the opinion that the Effects themselves performed the Summon, that it was not a manual player action.

TL;DR: in Edison Format, a Summon performed by "Ultimate Offering" / "Mausoleum of the Emperor":

• cannot be negated by "Solemn Judgment"!
• can be responded to by "Torrential Tribtue" if "Ultimate Offering" was Chain Link 1.

Likewise, "Solemn Judgment" cannot negate the Synchro Summon performed by "Urgent Tuning" (even if it was Chain Link 1).
Read more below for references!

• "Mausoleum of the Emperor and Ultimate Offering generate Effectual Summons, even though they are not Special Summons. [...] and those summons cannot be negated. You must negate the effect causing the summon." - Jiggy-Ninja (July  9, 2007) [REF]
• "Actually, the monster Normal Summoned by Mausoleum of the Emperor is Summoned by Mausoleum's effect, similar to Ultimate Offering's effect. Since it is the effect of a face-up Spell/Trap Card, Solemn Judgment cannot be activated." - ness00 (May 20, 2009) [REF]
• "Parallel to inherent and non-inherent Special Summons, inherent and non-inherent Normal Summons exist. Non-inherent Normal Summons are a special form of the Normal Summon. They are performed by cards such as "Ultimate Offering" and "Gemini Summoner". The Game Mechanic to negate those Summons is the same as with Special Summons. Therefore, you CANNOT negate a non-inherent Normal Summon with "Solemn Judgement" as the non-inherent Normal Summon is performed in a resolving chain." [REF]
• "Officially, in the OCG, Konami has not said anything either way about this (Horn of Heaven vs. Ultimate Offering) yet, though. However, unofficial sources like the JERP agree, that "Horn of Heaven" can negate such a Normal Summon. [...] the JERP lists that "Ultimate Offering" works this way, even though the JERP hasn't been updated since POTD - before Synchro Monsters existed." Entropy / Deus Ex Machina (June 29, 2009) [REF]
• "The Normal Summon is performed through Ultimate Offering's effect. You cannot activate Solemn Judgment during the resolution of an effect. This is true for both the TCG and OCG. This is different from the Urgent Tuning ruling, in case you were comparing it to this scenario." - ness00 (Sept 24, 2009) [REF]
  
• "Apparently, Ultimate Offering's and Urgent Tuning's Summons aren't performed through a Card effect, so they can be negated by some Cards like Solemn Judgment. This doesn't apply to the TCG." - ness00 (Jan 6, 2010) [REF]
• Concerning Ultimate Offering and Mausoleum of the Emperor: "Both of their effects start chains, and "Solemn Judgment" cannot interrupt the resolution of the effect." - Redshift (Sept 4, 2010) [REF]
• Concerning an OCG ruling that Solemn Warning could negate a Summon performed by Chain Link 1 Ultimate Offering:  "OCG ruling, it doesn't apply in the TCG yet." - ness00 (Jan 23, 2012) [REF]
• Solemn Warning: "Cannot negate a Normal Summon through Ultimate Offering.  (Same reason Rai-Oh cannot negate a Special Summon through Monster Reborn)." YuGiOh Rules Theory (May 5, 2013) [REF]