No because when the phase spiders emerge in the PC's area they are not hidden and thus automatically notice each other.
Surprise: If neither side tries to be stealthy, they automatically notice each other. Otherwise, the DM compares the Dexterity (Stealth) checks of anyone hiding with the passive Wisdom (Perception) score of each creature on the opposing side.
Wrong.
They are stealthy by virtue of being on a plane where they cannot be seen or heard (but they can see the characters).
Consider an Rogue/assassin. He surprises a monster (having used Stealth successfully). In the first round of combat, he wins initiative and runs screaming at the monster in full line of sight and attacks. Is the monster still surprised? Yes. Unlike Hidden, the state of surprise does not end when foes become visible. It ends after the surprised creature takes its first turn.