Those "fingers" that fell off won't grow - they aren't attached to a part of the stem so won't have any eyes. Whoever told you they would grow doesn't know much about dahlias- or was lieing to you.
Did you see any eyes- or shoots on the tubers that you planted? How soon they come up depends on how deep you planted them & how warm it is where they are planted- dahlias like the ground to be about 60* - if it's cold & wet they'll likely just sit there & not grow until the ground warms up- or they'll rot if it's really cold & wet.
Ellie

Thanks Ellie, I feel rather let down by the supplier. Oh well! The tubers themselves were planted with the eyes about 3-4 inches below the surface. The temp has warmed considerably here in the last week or so but I dont know the soil temp exactly. I shall wait and see. I have dedicated quite a large area to dahlias so hopefully they will come on strong. Thanks again. Kat