All shrine blessings in vanilla Skyrim, Dawnguard, and Dragonborn, plus the Blessing of the Stag Prince effect you get from wielding the "Glass Bow of the Stag Prince" found in Dragonborn, are boosted by any Fortify Restoration alchemy effect on you at the moment you receive the blessing. The boosted magnitude sticks until the blessing is removed or refreshed, not when the potion effect runs out. The root cause is that the underlying magic effects of each blessing spell have their Magic Skill field set to 'Restoration', which allows the RestorationPowerMod entry within perk AlchemySkillBoosts to trigger. Setting the Magic Skill fields to 'NONE' or tightening up the entry point conditions within AlchemySkillBoosts should fix the issue.
The relevant magic effects:
<pre class="_prettyXprint">
DLC1FortifyMarksmanFFSelf (Auriel)
DLC2FortifyOnehandedFFSelf (Boethiah)
DLC2FortifySpeechcraftFFSelf (Mephala)
DLC2ResistMagicFFSelf (Azura)
FortifyBlockFFSelf (Stendarr)
FortifyHealthFFSelf (Arkay)
FortifyMagickaFFSelf (Julianos)
FortifyMagickaRateFFSelf (Akatosh)
FortifyPersuasionFFSelf (Dibella)
FortifyRestorationFFSelf (Mara)
FortifyShoutTimerFFSelf (Talos)
FortifySneakFFSelf (Nocturnal)
FortifySpeechcraftFFSelf (Zenithar)
FortifyStaminaFFSelf (Kynareth)
dlc2MerchBowOfTheStagBlessEffect (Blessing of the Stag Prince)</pre>