Being able to see those telegraphed AoE's and markers are the byproduct of the WoL's Echo. Other characters in the franchise that do not possess an Echo cannot see AoE/ telegraphed attacks at all. It's a gameplay mechanic that is canonical for Echo users in-verse ( I'm getting undertale verse flashbacks oh no )
To contextualize:
The red marker hovering over the player in this recorded clip is called a Tank Buster. Mechanically speaking, it is a heavy-hitting attack that requires mitigation, healing, and shielding to endure. Otherwise, it is fatal to anyone that isn't a Tank. (And our recorder friend is a DPS class. Sucks to be them.)
Based on the examples linked by Shmooply, I'll address them in order starting after the Tank Buster link:
Example one, that's called a Flare Marker. It does damage based on ranged proximity. The closer you are to the object/player with the marker, the higher the damage. It's not dodge-able in most cases, but the further you are away, the less damage you take.
Example two, the one with the "arrows" is called a Stack Marker. It means that the attack requires more than one person to endure by standing close to one or more other players. In this case, WoL doesn't get the benefit of having another person to help. However have been instances of WoL enduring a stack marker without another person
by using Rubble/ Debris as a substitute if they lack player support.
Example three, same as Example two, except there's a beam being thrown.
Example four, that's called a Donut AoE. And for that clip in particular, the only safe spot is at point-blank range.
Example five, the "eye" is called a Gaze Marker. In the game, it means to point your character's front side away from the Marker or you'll incur a negative debuff, effect, or even damage. To dumb it down, in-game this is usually shown to indicate that "oh hey this monster can petrify or stun you. look away!".
And as to how how this all relates to WoL, it's part of his Precog / Info Analysis. The Echo automatically designates an attack by giving it a marker, AoE, or telegraphed danger areas like the examples above. He'll effectively be able to tangibly recognize what kind of attack it'll be off the bat, will be able to see the scope of Suika's attacks before they're thrown, and act accordingly before said attacks are executed.
Additionally, WoL knows how long wind-up/ charge-ups for attacks take,
such as Alexander's Timestop via Temporal Stasis. (It's indicated riiiiight next to his boss healthbar in the link. Look for the sudden orange-yellow bar that appears on the top part of the screen. )