The A/G sensing system on the 757 comprises tilt sensors on the main landing gear trucks, and strut compression sensors on the nose landing gear only. The later is only used for stall warning and portions of the warning/caution system.
Thrust reversers utilize the main gear tilt sensors, and can be deployed once the gear is untilted irrespective of the nose gear being on the ground.
Provided the speedbrake lever is in the armed position and the thrust levers are at idle, all 12 spoiler panels should extend as soon as the main gear untilts on the ground. Nomally, a failure in the automatic speedbrake system would result in both an Eicas advisory message and a caution light. In those circumstances the speedbrakes would (normally) be deployed manually after landing. If the speedbrake lever was not armed (in the down position,) there would be no caution or advisory message. If this were to be done intentionally or unintentionally, the spoilers would have to be activated manually on the ground.
Irrespective of the position of the speedbrake lever, as soon as the first thrust lever is moved to the reverse idle detent, the spoiler panels will fully extend and the lever will move to the up position.
This isn't to add any speculation to what might or might not have happened in this incident, but to clarify the system on the 757, that may well differ from some other aircraft types.