Sorry, the picture of you playing alto threw me off. Yes, that’s the fingering to use, but it sounds like you’re missing another note: add the index right hand finger to what you’re doing. (right hand index finger is the one that makes the low F note)
You can hit some form of F# with the 3 you’re using but it will sound really flat, then adding that index finger will bring it up a notch to get it in tune.