The name before the curly brackets is the unoriented name, and [unoriented name] {0,0, ..., 0} refers to the oriented link obtained by orienting [unoriented name] so that the resulting link has the same PD notation as that given at KnotAtlas.
For 1 ≤ i ≤ n-1, the ith position of the 0 in the (n-1)-tuple refers to the (i+1)th component of the link. Note that the order of the components appears in the (colored) diagrams as: BLUE, PURPLE, GREEN, YELLOW, RED. Changing the ith zero in the curly brackets corresponds to changing the orientation of the (i+1)th component. In particular, the blue component will not change orientation in our diagrams.
The oriented link L6a4{0,0} has the PD notation as given at KnotAtlas for L6a4 (the Borromean rings). In our diagrams, a 1 in the first or second entries of the pair corresponds to having changed the orientation for the purple or green components, respectively.