Ice Nova of Frostbolts and repeat mana cost

This does not actually happen.

Ice Nova of Frostbolts has a special behaviour explicitly described on the gem, where if cast on a frostbolt, the spell will not repeat, but the nova will occur again from the same frostbolt. When not cast on Frostbolt, it repeats normally.

Repeating means a single use of the skill plays the cast animation again, causing all effects of the skill to happen again. Ice Nova cast on frost bolt does not do that, instead you play the animation once and then after the nova happens, it just happens again without your character repeating anything.

What's actually happening in the linked video is you're spending mana more frequently when casting on the frostbolt because you are no longer repeating - rather than paying the cost and playing the animation twice, you're paying the cost and playing the animation once, but each animation is still giving you the second nova after the first from that cast. So you are spending more frequently, but also causing novas more frequently.