Does Witch Bolt deal the added 1d12 damage on the turn that it’s cast?

Assuming that Witch bolt is cast at 1st level and hits the target would the target take 2d12 damage in that turn because its the beginning of the spell’s duration and

"on each of your turns for the duration, you can use your action to deal 1d12 lightning damage to the target automatically."

or does it take effect the turn after you cast it?

How do attack rolls and criticals affect a 2d6 vs 1d12 damage roll? [duplicate]

For example, given the probability distribution between two similar weapons:


D&D 5E Weapons – Basic Rules pg.48:

Text


Damage Discrete Distribution – AnyDice:

Text2


Its evident that Greatsword is more reliable and has a higher mean damage roll.

But how does this change if we factor in an attack roll with some chance to hit? Do critical hits make the Greataxe preferential?

Is increasing the Primal Savagery spell’s damage die to 1d12 unbalanced/unnecessary?

The primal savagery spell states:

[…] Make a melee spell attack against one creature within 5 feet of you. On a hit, the target takes 1d10 acid damage…

The spell’s damage increases by 1d10 when you reach 5th level (2d10), 11th level (3d10), and 17th level (4d10).

Compare this to some other spells:

  1. Firebolt deals 1d10 fire damage from a range.
  2. Ray of frost deals 1d8 cold damage from a range and lowers the target’s speed by 10.
  3. Shocking grasp deals 1d8 lightning damage from melee and prevents the target from taking reactions, with advantage against targets wearing metal armor.
  4. Chill touch deals 1d8 necrotic damage from melee and prevents it from regaining hit points, also granting disadvantage to undead targets.

The primal savagery cantrip deals one die size additional damage (an average of +1 damage) and has no additional effects nor does it let you attack from a range. This feels particularly weak to me and so I wonder:
Would increasing its damage die to 1d12 (both the initial damage, and how it scales) be unbalancing or is the change simply unnecessary and the spell is already balanced against other cantrips?