Is the shifter clicking down, or is the chain dropping down with the shifter still in 2 ?
Could be that your mech is badly adjusted. In normal use will it shift between all three easily.
The shifter is clicking down and the chain drops on the number 1 ring if that makes sense.
This is key - there is no way the chain would move chainring without the cranks being turned. Therefore, as well as the shifter movement the cranks must be turned as well. I refuse to believe that a stationary bike would change gear itself and have the cranks rotated.