All the wizard needs to use his reaction is an attack that hits. This has nothing to do with whether or not he notices the assassin, himself.
So the assassin stays hidden for the duration of a single die roll? Is that what's bothering you? Because once the attack is made, it will either hit or miss. There is no third option. The attack roll determines whether the attack is a hit or a miss, so as soon as the attack is made (i.e. the moment the die is rolled at the table) this question has been resolved one way or the other.
This really gets to the level of abstraction in the D&D combat system and what the attack roll represents in the narrative. A lot of people that have written posts on ENWorld don't narrate every attack that hits as doing real physical damage. A "hit" needn't ever make actual contact to incur hit point damage. A character might experience a reduction in hit points because of the effort it takes to avoid a lethal blow, or have their resolve worn down by the attempts of their foe to strike them, the loss of that resolve represented by taking damage. Not until the final blow that drops that character to zero hit points is there any reason to narrate a "hit" as making physical contact. If you think about this, it makes a lot of sense. How many times do you think someone can be struck with a sword before they lose enough blood to fall unconscious? Probably not too many, and yet high level characters are able to absorb tens of "hits" from such a weapon with no impairment to their functionality. This is what the Basic Rules have to say about this issue:
So really the issue of narrating the "hit", and the logic of the resulting ability of a mage to cast Shield, is left entirely up to you as the DM, and any inability to credibly narrate these events is not due to any fault to be found in the rules as written, but is due entirely to a lack of imagination on the part of the DM.
Now you've jumped the shark, dude! When you are reduced to using "level of abstraction" to bolster you're otherwise counter intuitive, illogical BS, it's time to give it up. "Dungeon Masters describe hit point loss in different ways." So if I use a more simulationist approach as opposed to your abstractions, then the "hit" rule changes? Absurd! Your argument does not quote rules, it uses suggestions. My parting shot is simply this: People like me will never sit at your table and people like you will never sit at mine. Good riddance to this thread!