Auto speedbrake operates when:
Armed and speedbrake armed light illuminates
Thrust retarded to idle
Any gear strut compresses (for flight spoiler, right gear strut for ground spoilers)
Wheel speed greater than 60kts.
Probably after the bounce the system detected the wheel spin and as thrust was retarded that made the spoilers deploy.
If a shallow bounce were to occur it is important not to close the thrust but mantain the landing attitude and tocuhdown.
Hard bounce- go around