I am taking EXR files to photoshop for post processing, but I want the filmic color management applied. Is there a different file format I should be using, or is there a way to apply filmic color management to an EXR file?
Photoshop and other software of its ilk are display referred imaging applications. While PS will load an EXR, it does not possess the quality of controls one requires to properly manipulate scene referred photographic imagery.
To deal with a strictly display referred application and suffer as little quality loss as possible, save to a display referred format such as a 16 bit TIFF using the Filmic Base Log Encoding. It would then be possible to sculpt your own 'S' shaped curve to adjust contrast, or convert the Filmic set to the limited LUT format that Photoshop can understand.
DaVinci's Resolve has the granularity and more industrial tools to properly manipulate EXRs, although it will require a proper chain of nodes to do so. For further explanation along these lines, feel free to check Filmic's issue tracker where some help has been offered regarding the details of such an implementation.