This is referring to the arrow that appears on a duct or pipe connector icon in the family editor. This arrow indicates where the pipe or duct is...it must point toward the connecting pipe or duct. You can flip this easily when you place a connector on a face but not as easily when using the work plane option.
Connectors placed on a "work plane" define their "arrow" orientation based on the "positive" side of the Reference Plane used. The positive side of a Reference Plane is the left side of the "head", where the name appears (when you assign a name parameter to the ref plane). This is true for Reference Planes we add to a family. The stock reference planes that you find in the template behave the opposite way, go figure...positive is to the right side of the "head".
I suppose the connection arrow is just there to tease you in this instance. When the connector is applied to a "face" the "flip" arrow works. Remember the connection arrow represents the duct/pipe...it should point toward the connecting duct/pipe. Actual Flow direction is defined inside the properties dialog of the connector.
Oh...if the arrow is "wrong"...flip the reference plane, drag the end control grip at one end over the other, don't mirror because Revit will want to delete the connector.
Another worthy tip, brought to us by AUGI member Truevis aka Eric, is to use the "Split Face" tool on a face to define a portion of the surface to contain a connector as opposed to adding another solid to do so which you'll find in many of the stock families. May you "connect" well!