I love cases like this and I guess we just do things a bit different.
This is because we narrate and play the game with the mind set that
most things in the round are actually underway
at the same time. For example, today a monk wanted to move to engage an ogre and attack it. They were sixty feet apart (far enough, neither could move
and attack, except with Step of the Wind (not employed). However, I understand that from the moment the round begins, actions begin. Both opponents were moving towards each other and met roughly in the middle. The monk, who had the higher initiative, simply got his attacks in first.
So, if the players all fail perception such as in this case, (IMO) there is no twig-snapping, no seeing something out of the corner of your eye, etc. because if you think about it, the enemy is
still hidden and hasn't acted yet. With a failed perception, the PC has no idea where the attack is coming from or what is out there. But this is where the idea of simultaneous action comes in. I'll give you an example with some initiative totals:
Alice got 27.
Andy got 19.
Brenda got 16.
DM got 15.
Bob got 9.
Chuck got 3.
DM narrates after initiative is rolled: "Alice, you see bushes part and leaves fall as several giant spiders and two ettercaps emerge for hiding, moving towards the party to attack! (Note: the monsters are
starting their actions, but none get resolved until their initiative comes up.) The rest of you fail to notice the threat."
Alice: "I move to the edge of the path, back to the tree, and wait for the first enemy to come within reach so I can attack it."
Brenda: "I'm not surprised now, so I can cast Shield if I have to."
DM: "Yep. Ok, Alice, a giant spider strides past you, heading towards Bob!"
Alice: "I lunge out an stab it!"
(Alice hits!)
DM: "Good damage! The spider staggers and sticky goo clings to your blade as you pull it back. Brenda, an Ettercap jumps towards you, biting and clawing! The bite hits!"
Brenda: "I throw up my hand, casting
Shield."
DM: "The ettercap's attack glance off of the shimmering barrier, but it eyes you with a hateful hunger."
(and so on...)
So, technically, once the action begins and the monsters are moving (no longer in stealth and hidden), Alice
is aware of them and able to act quickly enough. But, until that moment she wasn't. We don't play it as a sixth-sense or anything else, but that it perfectly fine, too. Others might play this as:
(After initiative is rolled.)
DM: "You sense something is wrong, what do you do?"
Alice: "I don't see anything yet, so I'll move to the edge of the path near a tree and get ready to strike."
Brenda: "Nothing, huh? Well, I trust her instincts and have my Shield spell if I need it."
(and continue as before...)
Obviously both work fine, we just prefer to have the action more "all at once" most of the time if it makes sense since although the rounds are discrete, the action usually isn't IME.