If you are using Google Photo to backup your photos, you should also use it as your "gallery" app on your phone to manage photos.
When you delete a photo in the Google Photo app, it will delete it in Google Photo's online storage as well. Actually, it places it in Google Photo's "Trash" folder, where it is held for 60 days unless you manually purge a picture or the entire folder's contents.
To my knowledge, this is just the way it is and is by design, there are no options to do anything differently. It is designed to be your "recovery" for photos in case you lose them by any means... How is Google Photo supposed to know if you deleted that photo purposely, or by accident.