copper pour+direct connect via
The fanout command will not connect to polygon pours automatically. However, when you pour the polygon, you can specify whether you want the polygon to direct connect, or thermal connect to the polygon. In the Design Rules, you can choose the width of the thermal relief spokes, and whether you want four or two spokes. The rule is found under "Design>>Rules>>Plane>>Polygon Connect Style".
Note that you cannot create the polygon as part of the footprint. Footprints are only allowed to use "Copper Regions", not "Poured Polygons". The polygon has to be placed after you've put the footprint on the PCB.
To summarize, the polygon controls the connections to pads, not the fanout command.