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The vampire is destroyed

The combat rules on p. 197, PH say:

Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws.

The sunburst spell's effect is instantaneous, but so is the damage. There is no time delay given in the rules between an attack or spell hitting or causing a saving throw, and the resulting damage. With no defined difference in timing, it all must happen in the same instant.¹

That means the vampire is in sunlight at the instant where it takes damage, and cannot transform to mist but instead is destroyed, if the damage reduces it to 0 hit points.

Because the rules also do not explicitly say that there is no time delay, you might want to check with your DM in advance if they rule this way if you are unsure about how they would handle it.

¹ The rules might allow other things to happen in that same instant. The way the game resolves them is by ordering them in some kind of sequence. For example, if you get hit by an attack, you can react with a shield spell before taking damage, because the spell says so. See also Are getting hit and taking damage simultaneous events? (note that the accepted answer is not the majority answer by wide margin; thanks to @Kirt for digging up that Q&A).

The vampire is destroyed

The sunburst spell's effect is instantaneous, but so is the damage. There is no time delay given in the rules between an attack or spell hitting or causing a saving throw, and the resulting damage. With no defined difference in timing, it all must happen in the same instant.¹

That means the vampire is in sunlight at the instant where it takes damage, and cannot transform to mist but instead is destroyed, if the damage reduces it to 0 hit points.

Because the rules also do not explicitly say that there is no time delay, you might want to check with your DM in advance if they rule this way if you are unsure about how they would handle it.

¹ The rules might allow other things to happen in that same instant. The way the game resolves them is by ordering them in some kind of sequence. For example, if you get hit by an attack, you can react with a shield spell before taking damage, because the spell says so. See also Are getting hit and taking damage simultaneous events? (note that the accepted answer is not the majority answer by wide margin; thanks to @Kirt for digging up that Q&A).

The vampire is destroyed

The combat rules on p. 197, PH say:

Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws.

The sunburst spell's effect is instantaneous, but so is the damage. There is no time delay given in the rules between an attack or spell hitting or causing a saving throw, and the resulting damage. With no defined difference in timing, it all must happen in the same instant.

That means the vampire is in sunlight at the instant where it takes damage, and cannot transform to mist but instead is destroyed, if the damage reduces it to 0 hit points.

Because the rules also do not explicitly say that there is no time delay, you might want to check with your DM in advance if they rule this way if you are unsure about how they would handle it.

The vampire is destroyed

The combat rules on p. 197, PH say:

Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws.

The sunburst spell's effect is instantaneous, but so is the damage. There is no time delay given in the rules between an attack or spell hitting or causing a saving throw, and the resulting damage. With no defined difference in timing, it all must happen in the same instant.¹

That means the vampire is in sunlight at the instant where it takes damage, and cannot transform to mist but instead is destroyed, if the damage reduces it to 0 hit points.

Because the rules also do not explicitly say that there is no time delay, you might want to check with your DM in advance if they rule this way if you are unsure about how they would handle it.

¹ The rules might allow other things to happen in that same instant. The way the game resolves them is by ordering them in some kind of sequence. For example, if you get hit by an attack, you can react with a shield spell before taking damage, because the spell says so. See also Are getting hit and taking damage simultaneous events? (note that the accepted answer is not the majority answer by wide margin; thanks to @Kirt for digging up that Q&A).

The vampire is destroyed

The combat rules on p. 197, PH say:

Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws.

The sunburst spell's effect is instantaneous, but so is the damage. There is no time delay given in the rules between an attack or spell hitting or causing a saving throw, and the resulting damage. With no defined difference in timing, it all must happen in the same instant.

That means the vampire is in sunlight at the instant where it takes damage, and cannot transform to mist but instead is destroyed, if the damage reduces it to 0 hit points.

The vampire is destroyed

The combat rules on p. 197, PH say:

Most DMs have a monster die the instant it drops to 0 hit points, rather than having it fall unconscious and make death saving throws.

The sunburst spell's effect is instantaneous, but so is the damage. There is no time delay given in the rules between an attack or spell hitting or causing a saving throw, and the resulting damage. With no defined difference in timing, it all must happen in the same instant.

That means the vampire is in sunlight at the instant where it takes damage, and cannot transform to mist but instead is destroyed, if the damage reduces it to 0 hit points.

Because the rules also do not explicitly say that there is no time delay, you might want to check with your DM in advance if they rule this way if you are unsure about how they would handle it.