The additional mana is paid at the same time the spell/ability is announced. [bethmo 1996/06/20]
The extra mana is not considered part of the mana cost (see Rule G13.7). A Spell Blast would still only require the original mana cost as X in order to counter the spell. [Aahz 1994/09/02]
The extra mana is not considered part of the activation cost. It is a separate cost. [Aahz 1994/09/02]
The extra mana is part of the play cost, so cost reducers like Helm of Awakening can be used to pay part of this cost.