Cant make a proper Vortex effect with objects and curve

I want to do kinda similar effect (starts from 1.16) https://www.youtube.com/watch?v=PYHOV3bVIG0

... but with exception that I want not particles but full objects to be attached to the curve so they will rotate and move the way of the curve. So I created a bezier curve, but the problem is they become completely flat (eg. plane instead of cube) and move very jerky. Any recommendations to fix it? I guess the 2nd problem is easy to solve in animation editor but don$$$$t know about the 1-st one