Eagle 20EW Specialty Fungicide cannot be used as a soil drench, according to the manufacturer. They recommend that you use Eagle 20EW as a foliar spray or topically on the soil.
No, Eagle 20EW is not labeled for mahonia specifically.
A product that is labeled for it is Ferti-Lome Broad Spectrum Landscape and Garden Fungicide, and it does treat rust on it.
Eagle 20EW is used on golf course fairways, roughs, tees and greens, commercial and residential stone fruit trees, apple trees and grapes, and other landscape ornamentals. For use on ornamentals such as chrysanthemums, daylilies, poinsettias and roses in nurseries, landscapes and greenhouses. Please refer to the product label for specific application instructions. We do carry fungicides that are safe to apply on tomatoes. Please click the link below for additional information on the products that we do carry for them. If you have any questions, please let us know.
http://www.domyownpestcontrol.com/edible-garden-products-c-59_481.html