Simultaneous events require a DM decision
'Anytime After', 'Right After', and 'Immediately After'
Sometimes a feature triggers an event that comes after it, but may occur any time later during the same turn. The Great Weapon Master Feat, for example, says:
On your turn, when you score a critical hit with a melee weapon or reduce a creature to 0 hit points with one, you can make one melee weapon attack as a bonus action.
What is permitted to happen between your critical hit and your bonus action weapon attack? Could you, for example, hit, then move, then take your bonus action?
Sage Advice Compendium explains that movement or anything else between the hit and the bonus action it grants is permitted so long as the bonus action still occurs on your turn:
You take the bonus action on your turn, anytime after you hit with the attack that grants the bonus action. So yes, you can move before taking the bonus action (if you have movement remaining).
Readied actions, however, are different. Readied actions follow the timing rule that:
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger.
The SAC explains that 'right after' means 'immediately after':
A readied action occurs immediately after its trigger. If you defined the trigger as an attack, your action happens after that attack.
and
Unless a rule tells you otherwise, a reaction occurs immediately after its trigger.
So, 'right after' is synonymous with 'immediately after' (and thank you to a comment from Mołot on my since-deleted answer explaining this to me). As a readied action, the thug's crossbow shot will occur 'immediately after' its trigger, which is the movement of the sorcerer. What does immediately mean? It means that normally no other event can occur between the two.
However, the reaction of the thug is competing with the sorcerer casting their spell, which is also immediately after their movement.
you can use a bonus action on your turn to cause whirling gusts of elemental air to briefly surround you, immediately before or after you cast a spell of 1st level or higher. Doing so allows you to fly up to 10 feet
If the sorcerer's movement is immediately before their spell, then their spell is immediately after their movement. If their movement provokes the thug's reaction, the crossbow shot is also immediately after the sorcerer's movement. Once the sorcerer moves, we have two events, both of which occur immediately.
When simultaneous events are competing for resolution, the DM decides which one has priority. In the case of the sorcerer, RAW is that the DM will decide whether the sorcerer gets to cast his spell, and then gets knocked unconscious, or whether the crossbow shot will resolve first, knocking the sorcerer unconscious, and rendering him unable to cast.
Since the release of XGtE, an optional rule is that the player whose character's turn it is decides the order of resolution among simultaneous effects. In this case, the player of the sorcerer would decide, and would likely choose to cast their spell first. This is an optional rule, though, and not RAW.
My reading of RAI is that the spell cast goes first
I believe that in this case, it is intended that the sorcerer gets to cast before the thug can take their reaction. Helpful comments from Eddymage and Mołot on a previous answer have clarified for me that this is my interpretation of RAI rather than RAW.
I find the following arguments compelling, but you may not:
FIRST, the movement granted by Tempestuous Magic does not provoke opportunity attacks (and this is common among things that grant immediate movement, such as the Relentless Avenger class feature and several spells). Opportunity attacks are in some sense "faster" than reactions, because while reactions occur immediately after their trigger, opportunity attacks by definition actually interrupt their trigger. From the SAC:
when a reaction has no timing specified, the reaction occurs after its trigger finishes (DMG, 252). In contrast, an opportunity attack specifically takes place before its trigger finishes—that is, right before the target creature leaves your reach (PH, 195).
Normally, a creature using its own movement does provoke opportunity attacks (SAC):
For example, the effect of the antipathy/sympathy spell requires the target to use its movement, meaning that it would provoke opportunity attacks when it does so. Similarly, dissonant whispers requires the target to move using its reaction (if available), so that activity also provokes opportunity attacks.
To summarize, opportunity attacks are faster than reactions, and normally one's own movement provokes opportunity attacks. But in the case of the tempestuous magic, the movement granted does not provoke opportunity attacks. That, to me, is at least a clue that it is even faster than something that is itself faster than a reaction. In a competition between simultaneous events, the tempestuous movement should beat the readied action to shoot the crossbow.
SECOND, as a basic design principle, a class feature should not promote paradoxes. It is an interesting choice to say that casting a spell permits additional movement, but that movement can come before the spell. To me, that only makes sense if the movement is so tightly connected to the spell that it can't be interrupted. To rule otherwise invites paradoxes.
You are allowed the extra movement immediately before you cast a spell but only because you will cast the spell. The movement occurs
immediately before or after you cast a spell
and not immediately before you "attempt" to cast a spell or "intend" to cast a spell. If you don't end up casting a spell, you can't use the feature, because it is the casting of the spell that grants you the bonus action you can use to move. Without casting the spell, you don't have the bonus action to begin with. But if that movement could provoke a reaction that resulted in you losing consciousness as OP posits, then you would not be able to cast the spell that permitted you to take the movement. But if you couldn't take the movement, then you would not have provoked the reaction which removed your ability to cast the spell, so you could cast the spell, meaning you could take the movement...
I don't think the feature is supposed to invite such paradoxes, and the only way to keep it from doing so is to make sure nothing can happen between the movement and the casting of the spell that happens immediately after.
It is at least RAW that the DM will need to decide between these two simultaneous events, but I think other clues point to the intent being that the spell will happen before the thug's reaction.
