We had this argument at work today.

In an Multiplayer game my friend attacked another. he played Heat Vision exhausting his defender. In response my friend used Dazzler's ability to exhaust said defender making Heat Vision "fizzle" out.

Then the great debate started. I said that Since my friend had priorty that his Dazzler would take effect over the Heat Vision and the character would already be exhuasted making HEat Vision not work.

Everyone else said that since part of the payment for Heat Vision was to exhaust the defender, that would take prioritry and Dazzler couldn't use her ability.

Who was right?

You are correct. The 'cost' of exhausting the defender for Heat Vision is actually part of the effect. Compare this with Heroic Sacrifice, which has both a true cost and an effect that often gets confused with the pseudo-costs like in Narrow Escape and Heat Vision.

To clarify, the character needs to be exhausted, but unlike a true cost, you don't exhaust the character until the effect resolves. This means that unlike a card like Mystical Paralysis, you have a priority point to use an effect to exhuast the character before the effect can attempt to resolve and charge the 'pseudo-cost'.