Yes, delayed damage is enhanced
No matter if a spell does its damage instantly or after some time, that damage is still dealt by the spell.
Since the potion affects the damage dealt by the spell, and since delayed damage is still the spell's damage, then the potion should also affect this delayed damage.
The argument of "when you cast"...
It could be defended that the potion mentions that this change in damage calculation happens "When you cast a spell..." (or, more specifically, "The first time you cast a [...] spell").
It then seems valid to assert that this calculation modification only applies to rolls done while casting.
This Q&A discusses in more details the exact timing of "when" a spell is cast. The global consensus seems to be that you are only casting a spell during its casting time, and holding concentration does not count as casting.
As such, damage rolls done during the next turns shouldn't be affected by the potion... Right?
... contradicts itself.
There is a flaw with this reasoning, however. Even spells that only deal damage instantly do not roll their damage during casting, but rather after the casting is complete and the spell resolves.
If we apply our previous logic to this situation, the original damage is not rolled during casting. As such, the potion may not apply its effect to a spell's instant damage.
This would mean that the potion can never apply its effect to a spell's damage, which defeats the point of the potion existing itself. There is a contradiction here.
With this, I conclude that the potion should enhance the delayed damage of a spell, even though that damage isn't done on the same turn as the turn when the spell is cast originally.