Without getting too into the weeds here, yes, the short answer is to adjust the Wipe Center controls in the effect.
Effects with internal position controls like this operate in composition space, so they don't necessarily pay attention to the positioning of your layer (unless you tell them to).
Here are two layers that both have Radial Wipe applied, with no changes made to that Wipe Center property. Notice how they're both originating from the center of the composition, even though the circle has been moved? (I added a low-opacity copy of the circle provided for context.)

If you want the effect to follow your layer, you need to tell it to do so, using a simple expression.
In the timeline, open up those effect controls.
Alt/Opt click on the stopwatch for the Wipe Center, grab the pickwhip (little swirlie icon) and connect it to the layer's Position property.

Alternatively, you can save a step by just grabbing the property pickwhip (NOT the layer parenting pickwhip), and making this same connection.

Your Radial Wipe effect will now follow the layer whereever it goes.