How does the lead polarity work on a D'Arsonval galvanometer?
The orientation N and S of the movement electromagnet are determined by the direction of the current and the winding direction. This can be easily remembered using the right-hand grip rule.



Figure 1. The right-hand grip rule: with fingers wrapped in the direction of current flow the thumb points in the direction of the field (N). Source: OneSchool.

With a little thought it can be seen that the illustration in the question is correctly drawn and that the north pole of the momement is at the top.


  I notice that the N polarized part of the coil is connected to the positive lead ...


Not quite right. The N isn't "connected" - it is a result of current flow and winding direction. There is no electrical connection as the wire is insulated.



Figure 2. Another D'Arsonval galvanometer movement diagram showing the springs. Source: Engineer's Edge

As current is increased the like poles repel introducing a turning moment which acts against a spring to give a rotation proportional to the current.