For Sphere or Resistance I am quite sure that you would have to pay the additional 1 mana. I did a bit of searching while looking for the answer to my question and this handy example popped up.
(Excuse my editing here, but it seems worthwhile to include the rule that actually describes the cost being locked in  --Clariax)409.1f. The player determines the total cost of the spell or ability. Usually this is just the mana cost (for spells) or activation cost (for abilities). Some cards list additional or alternative costs in their text. Some effects may increase or reduce the cost to pay, or may provide other alternative costs. Costs may include paying mana, tapping permanents, sacrificing permanents, discarding cards, and so on. The total cost is the mana cost, activation cost, or alternative cost (as determined in rule 409.1b), plus all additional costs and cost increases, and minus all cost reductions. If the mana component of the total cost is reduced to nothing by cost reduction effects, it is considered to be 

. It can't be reduced to less than 

. Once the total cost is determined, it becomes "locked in." If effects would change the total cost after this time, they have no effect.
409.1g  If the total cost includes a mana payment, the player then has a chance to play mana abilities (see rule 411, "Playing Mana Abilities"). Mana abilities must be played before costs are paid. 
409.1h  The player pays the total cost in any order. Partial payments are not allowed. Unpayable costs can’t be paid.
Example: You play Death Bomb, which costs  and has an additional cost of sacrificing a creature. You sacrifice Thunderscape Familiar, whose effect makes your black spells cost  less to play. Because a spell’s total cost is "locked in" before payments are actually made, you pay , not , even though you’re sacrificing the Familiar. 
I also have a similar question regarding additional costs that is slightly different. Say I have a Tidehollow Sculler in play and I cast something like Shrapnel Blast or Tinker. Does my opponent get the card back in his hand from the leaves play ability of Sculler, does my "sac as an additional cost" spell resolve first, or do I get to chose the order they stack in?
409.1i  Once the steps described in 409.1a–h are completed, the spell or ability becomes played. Any abilities that trigger on a spell or ability being played or put onto the stack trigger at this time. If the spell or ability’s controller had priority before playing it, he or she gets priority. 
It isn't specifically an ability that triggers on a spell being played, but the specific spell itself does trigger it. I think Shrapnel Blast/Tinker would go on the stack and then Tidehallow would so my opponent gets the card back in his hand before my original spell resolves but I would like some verification. Thank you. 
