All the damage from one attack roll or save applies at once.
When an attack deals multiple types of damage, all that damage is applied to the target at once.
In the case of your example, the total amount of damage taken by the attack is 91 + 85 damage (176 damage). The unfortunate PC makes a single saving throw, fails, and takes the specified damage. Only one save is made, so the damage hits as one and therefore becomes unconscious.
Let us take a different example; eldritch blast. At higher levels, eldritch blast can fire multiple beams, each rolling a separate attack roll. If a PC is attacked by two beams, and was brought to 0 hp by the first beam, but then is hit by the second, it would be a failed death save. This is because it counts as two separate attacks.
The reason it is split into separate damage types is for resistances and vulnerabilities. If your PC is resistant to a specific type of damage, then you can look at the separate damage types and apply the resistance to that portion of the damage roll.
The fact that the damage for Meteor Swarm is split into two numbers has no effect on the number of attacks/saves rolled, and so it all registers as one hit.