Mighty Summoner says (emphasis mine):
Any beast or fey summoned or created by a spell that you cast gains the following benefits: [...]
Faithful Summons says (emphasis mine):
If you are reduced to 0 hit points or are incapacitated against your will, you can immediately gain the benefits of conjure animals as if it were cast using a 9th-level spell slot.
Does the phrase "as if it were cast using a 9th-level spell slot" indicate that we should treat this as if we are casting the spell, thereby allowing us to apply Mighty Summoner to the creatures summoned?
Note, this question is different from this Q&A, as it is unclear if Faithful Summons counts as casting a spell: Would the 6th level Shepherd Druid's Mighty Summoner feature works on summoned creatures not made from spells