spider-sense is just feeling the wind the way she feels the earth. they even mention it in korra as an airbender power, though they bullshittedly imply being bald would help (hairs help you feel wind, so no). it's the same sense fish have that stops them bumping into shit.
the symbiote permanently left peter thinking of it as part of his own nervous system, so he doesnt worry about it coming at him and disturbing the air. so it might work that way with toph but her sense is a bit more deliberate and active, so if she concentrated at all she'd still be able to see it
then again, i wonder if the symbiote could shift itself into a helicopter and fly and why am i still imagining this