Official Riftbound ruling

How does it work if I cast Abandon while having an empowered Mel, Newly Awakened but they Rebuttal my spell?

In the case of Rebuttal, gaining control of a spell is not the same thing as countering that spell. Effects that prevent spells being countered don’t prevent their controller from changing. If Rebuttal is played choosing your spell, and they pay Any RuneAny Rune during resolution of Rebuttal, they will gain control of it. However, them not paying Any RuneAny Rune does not mean the spell will be countered.

Riot's question and answer, word for word, from theVendetta Rules FAQ and Clarifications

The cards

  • Abandon
    Abandon

    Spell

    Reaction (Play any time, even before spells and abilities resolve.)

    Counter a spell. Return it to its owner's hand instead of putting it in their trash.

    Predict. (Look at the top card of your Main Deck. You may recycle it.)

  • Mel, Newly Awakened
    Mel, Newly Awakened

    Unit

    When you play me, draw 1.

    Empower 3 Energy3 Energy (3 Energy3 Energy: Empower me. Use only if not Empowered.)

    Empowered Your spells and abilities can't be countered. If a spell or ability you control would give -MightMight to a unit it chooses, it gives an additional -1 MightMight.

  • Rebuttal
    Rebuttal

    Spell

    Reaction (Play any time, even before spells and abilities resolve.)

    Choose a spell with Energy cost no more than 4 Energy4 Energy. You may pay Any RuneAny Rune. If you do, gain control of it and you may make new choices for it. Otherwise, counter it.