How can I make a droplet save a modified file next to the original file?

Question

I am having a problem getting a Photoshop Droplet save a modified file next to the original file. That is, when I drag a file "page_6.pdf" from some directory onto my droplet, I want it to do its work and save a modified "page_6.psd" in that same directory.
This isn't working for me on Photoshop CC 2014 on Mac OS 10.10.
I have an Action which has an Open command, with the filename "page_1.pdf". Then it has a bunch of editing commands. Then it has a "Save As... Photoshop format" command, and a Close command. When I run this action within Photoshop, it brings up Open and Save As dialogues, and works fine.
In creating the droplet, I used File... Automate... Create Droplet..., and selected the following options:
Override Action "Open" commands
Destination menu value = Folder
Using Choose... button, select an output folder, Directory_1/ .
Check Override Action "Save As Commands" is checked
For File Naming, I use [Document Name] + "_deleteme" + [extension]
When I drag a folder, say "page_5.pdf" from some directory onto the droplet, Photoshop runs the Action on the document. However, it saves the modified document in Directory_1/, regardless of where the original file came from. And it always names the modified document "page_1_deleteme.psd", instead of using the Document Name of the original file.
If I modify the Open command in the Action to mention a different file, then the droplet always names the modified document with that name. It's as if Document Name in the File Naming dialogue always reflects what's in the Open command in the Action.  But -- I asked the droplet to Override Action "Open" commands!
When I set the Destination menu value to "Save and Close", then when I drag a file onto the droplet, the droplet opens a File Save dialogue and forces me to tell it where to store the file.  I don't understand this behaviour, and have a hard time reconciling it with the documentation at Photoshop Help | Processing a batch of files .
(Interestingly, when Destination menu value = None or Save and Close, Photoshop displays an alert about overwriting an existing droplet when I click OK to save. But when Destination menu value = Folder, there is no alert about overwriting existing droplet.)
How can I set up a droplet so that it writes the modified file in the same directory as the original file, and with the same root filename, but a different extension to reflect the different output file format?
Has anyone else made a droplet behave this way on Photoshop CC 2014 on Mac OS X 10.10?
Thanks in advance for your help.

Answer 1

Thanks for your insights.
Does my Action need to include an Open command?  I sure thought so, because of how the Photoshop Help | Processing a batch of files documentation describes 'Override Action “Open” Commands'.
"...If the action contains an Open command that opens a saved file and you don't select this option, the Batch command opens and processes only the file you used to record the Open command..." I don't want to operate only the file I used to record the Open command. However, this sentence doesn't say that an Open command should be part of a droplet Action.
"...Deselect this option if the action was recorded to operate on an open file..."  Maybe I if I rethink my Action as operating on an open file, then the Droplet will take care of the Open for me.  However, I have less control over the options the droplet's Open command uses.
I'll try disabling the Open command, and create a Droplet with that.