What kind of cost is the effect on Trinisphere?
Trinisphere's ability is an effect that directly changes the cost and takes place after all cost reductions and increases have been taken into account.
This is covered in the rulings on it's gatherer page:

Trinisphere’s ability affects the total cost of the spell. It is applied after any other cost increasers or cost reducers are applied: First apply any cost increases. Next apply any cost reducers. Finally look at the amount of mana you have to pay. If it’s less than three mana, you’ll pay three mana.
Even with a cost reducer on the battlefield, spells can’t cost less than three mana to cast.
If a spell costs at least three mana due to additional costs, such as kicker costs, that’s fine.

So to simply determine the costs for spell that you cast normally while a Trinisphere is on the field you can:

Start with the mana cost or alternate cost of the spell. (Temporal Mastery's Miracle is an alternate cost.)
Add any additional costs (Kickers, Replicate, etc.)
Add any cost increases (effects like Chill).
Subtract any cost reductions (effects like Baral, Chief of Compliance).
Check to see what the total cost of you spell is, if it is 0, 1 or 2 CMC you will pay 3 instead. If it is 3 or more CMC you will pay that cost.

Note that this order is the same order outlined in the comprehensive rules (emphasis mine):

601.2f: The player determines the total cost of the spell. Usually this is just the mana cost. Some spells have additional or alternative costs. 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 or alternative cost (as determined in rule 601.2b), plus all additional costs and cost increases, and minus all cost reductions. If multiple cost reductions apply, the player may apply them in any order. If the mana component of the total cost is reduced to nothing by cost reduction effects, it is considered to be {0}. It can’t be reduced to less than {0}. Once the total cost is determined, any effects that directly affect the total cost are applied. Then the resulting total cost becomes “locked in.” If effects would change the total cost after this time, they have no effect.