I use a File Watcher defined as this
Here is my watchers.xml file: 
<?xml version="1.0" encoding="UTF-8"?>
<TaskOptions>
  <TaskOptions>
    <option name="arguments" value="fix $FileDir$/$FileName$ --verbose " />
    <option name="checkSyntaxErrors" value="false" />
    <option name="description" />
    <option name="exitCodeBehavior" value="ERROR" />
    <option name="fileExtension" value="php" />
    <option name="immediateSync" value="true" />
    <option name="name" value="PHP CS Fixer" />
    <option name="output" value="" />
    <option name="outputFilters">
      <array />
    </option>
    <option name="outputFromStdout" value="false" />
    <option name="program" value="/usr/local/bin/php-cs-fixer" />
    <option name="scopeName" value="Project Files" />
    <option name="trackOnlyRoot" value="false" />
    <option name="workingDir" value="$ProjectFileDir$" />
    <envs />
  </TaskOptions>
</TaskOptions>
While autosave executes, sometimes I am getting an error message about the conflict between changes in memory and on disk.
How can I solve this issue?


 
                        
It happens because PHP CS Fixer modifies the file, as @LazyOne said, but you have empty value of "Output paths to refresh" so IDE cannot know about these changes.
Set the value of "Output paths to refresh" to
$FileName$- same as in arguments - to make PhpStorm aware about the changes (it depends on the "Working directory" value which has been set in Other Options - if it is set to $FileDir$ then you don't need to mention it in the paths to refresh).