But the Shield spell doesn't state this. Nor does Uncanny Dodge.
Imagine a context where the GM says "It's the NPCs mage's turn. <rolls some dice> Tara, you take 11 hp from magic missiles!" That would not be atypical in D&D play, at least as I've experienced it. Presumably it doesn't preclude Tara's player declaring a Shield spell. Or an Uncanny Dodge.
I think describing it as "time travel" is ridiculous whether or not the damage dice have been rolled. In the fiction, there's no difference between the
hitting and the
dealing of the damage. The latter is part and parcel of the former. The only reason it's an issue at the table is because - purely for gameplay reasons - there's a desire to draw a limit on player knowledge at one point rather than another. As I already posted, Rolemaster makes the player make the decision at the targetting step; and another option would be to insist that the player gets to know if the result is a hit or not, but not see the dice or know what AC has been hit by the attack, but the 5e rules simply don't prescribe the process in that degree of detail (in recognition of the fact that different D&D tables have long had different practices in this respect).
So at some tables Shield spells are occasionaly peirced by attacks (where the to hit result was 5 or more above what was needed) while at others, where the GM declares attacks in terms of AC struck, a Shield is never wasted (and this will nearly always be the way that
players declare attacks). Whether or not knowledge of the damage roll is also a factor in the decision-making about using a reaction is just another aspect of table practice (except for those cases where the rules expressly state the contrary).
Here is the text on reactions (Basic PDF p 70):
Certain special abilities, spells, and situations allow you to take a special action called a reaction. A reaction is an instant response to a trigger of some kind, which can occur on your turn or on someone else’s. The opportunity attack, described later in this chapter, is the most common type of reaction.
When you take a reaction, you can’t take another one until the start of your next turn. If the reaction interrupts another creature’s turn, that creature can continue its turn right after the reaction.
So there is no general rule that reactions happen after the trigger. You seem to be thinking of the "ready" action, which (p 72) involves declaring a "perceivable circumstance" as a trigger and which then allows the readied action to be taken "right after the trigger".
If a Shield spell or Uncanny Dodge worked in this way, then the trigger would have to be
being targetted by an attack as that is an (in fiction) perceivable circumstance which can be followed by creating an arcane shield or dodging the attack. But
a to hit roll succeeding is not an in fiction perceivable circumstance that occurs prior to the damage being rolled!
There is an in fiction perceivable circumstance that occurs between being targetted and being struck, which is something like "How dangerous the attack seems to be as it hurtles towards me!" But D&D doesn't have any procedural step of combat resolution that corresponds to this. (Contrast some other RPGs where, eg, this might be reflected by the number of dice in the attacker's pool.)
This means that if a player declares a readied action along the lines of "I leap in front of any attack against Tara that seems likely to do more than simply scratch her" I don't think the 5e rules provide any easy way to resolve that. Because we can't tell whether or not the attack is likely to do more than simply scratch Tara until we see the to hit and damage roll. At which point the "after the trigger has finished" rule suggests that Tara has been struck by the attacker and suffered the consequences of that.
