On the motor, the inner flange needs to be secured on the motor spindle at a position that allows the belt to close down until it's just clear of the motor spindle when the spring loaded outer is compressed.
Be very careful on how you try to compress the outer flange against the spring, the cast metal is very vulnerable to point loads, you need to apply pressure over as wide an area as possible.
On the lathe headstock spindle with the speed selection linkage in the low speed position the mechanically adjusted cone must be set so that the belt fits snuggly with its outer surface level (or nearly so) with the edge of the cones.
With the headstock cone set correctly the motor cone should be forced open to the point the belt is still gripped by the taper and its inner surface not in contact with the motor spindle.
Likewise in reverse, at the highest speed setting the belt should be still trapped by the cones and not riding on the lathe spindle.
Always rotate the mechanism whilst trying to adjust the speed, even if it's only by hand, it's the only way that the forces can direct the belt to ride up and down the cones, moving the change lever without doing this can wreck the change lever mechanism.
Reading through this saga may help Although problem cause by not servicing the machine and then fitting wrong length belt the words of caution, method of compressing spring to fit new belt and the pictures may help.