No,. The per-rest usages of these spells are independent from yourof the spell slots granted by the sorcerer class spells.
A sorcerer gets their spell slots from their Spellcasting class feature. These spells are cast using the sorcerer's spell slots, which depend on the sorcerer's level.
To cast one of these sorcerer Spells, you must expend a slot of the spell's level or higher.
These spell slots are specifically referring to the spells granted by the corresponding class:
In every case, the number of spells a caster can have fixed in mind at any given time depends on the character’s level.
By comparison, the Devil's Tongue trait makes no mention of classes or spell slots. In theory, a tiefling fighter could cast these spells just as effectively as a tiefling sorcerer of the same level. The tiefling's spells from Devil's Tongue are not cast using the spell slots of any class.
The trait is a special ability that lets creatures cast spellsspells without proper spell slots:
Some characters and Monsters have Special Abilities that let them cast spells without using spell slots. For example, a monk who follows the Way of the Four Elements, a Warlock who chooses certain eldritch invocations, and a Pit Fiend from the Nine Hells can all cast spells in such a way.
This ability is completely independent of spell slots gained from the tiefling's class levels.