By the rules, they can still reduce/avoid the damage.
According to the rules, both RAW and RAI, as long as your character is capable of reacting or moving (aka not affected by the Paralyzed, Petrified, Stunned, or Unconscious conditions), they are able to succeed on Dexterity saving throws. Not only that, but should they have the Evasion feature they can even avoid the totality of the damage directed at them. A good example of this is Viari in Acquisition Inc., who famously evaded a fireball that had filled an entire room. Now if you want to make sense of this, it'd be a good idea to look at how Dexterity ST work.
A dexterity saving throw means that through some level of agility or rapidity of action you can avoid a harmful effect. If we imagine this as moving out of the way, then we can interpret this as a character doing the following:
- Avoiding a projectile, debris, or a splash of some harmful substance.
- Moving behind some form of cover.
We can also consider this as the character being quick enough to either block part the effect or reduce its impact by:
- Catching or deflecting the source of damage (this would particularly apply to a Monk defending against Conjure Volley).
- Positioning themselves in such a way that they are less exposed to the effect (turning sideways, laying on the ground, etc).
- Reducing the damage by moving with whatever hits them (like a boxer rotating their head to reduce the impact of a blow).
Apart from positioning themselves in an optimal manner, this is much easier to visualize when we talk about something like shrapnel or debris that must be avoided, but becomes a lot more abstract when a spell that fills an area, in this case a fireball, is concerned. In this case, it may be better to rethink about the spell effect itself rather than the save. In the case of delayed fireball, the spell is seen as
[...] an explosion of flame that spreads around corners.
The explosion can manifest in different way. The fact that it spreads around corners discredits the idea that it's like a shrapnel grenade shooting off a multitude of firebolt-like projectiles, but it doesn't specify that the entire area is uniformly filled with fire. Indeed, it mentions that the fire spreads. Perhaps it does so in a manner that leaves some openings not filled by fire, or perhaps not all of the fire is equally as hot, much like a candle is hottest an inch above the wick. This could be how one avoids or reduces the damage caused by the spell.