Since oh-my-zsh is a more advanced zsh configuration, it should be simple enough to tell PHPStorm to use zshas a shell. This can be done in the "Settings" dialog box ("Menu File-> Settings") under "Project Settings->" Terminal. Just change the Shell Path to the path zsh(you can find out using type zshthe terminal).
To influence each (new) project, you may need to repeat this in the menu File> Default Settings
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