Chinook, I tested the hydrometer and it was accurate with plain ol' tap water.
The instructions you scanned said to rack into a carboy when SG is between 1.010 and 1.020. I am now wondering what the purpose of the secondary is? Why not leave it in the primary until fermentation is complete? Maybe because you have to open the primary to test the SG and therefore exposing it to more O2 than necessary?
The purpose of using a carboy (secondary fermentation vessel) is to limit the contact of air (read: O2) with the wine. At that stage of the game, oxygen is bad for your wine. A bucket has a large area and a large headspace, and O2 can get to your wine.