Creating automation/droplet for batch resizing and putting on background

First is the action, there are only 2 key steps for the resizing:

1) File > Automate > Fit Image commad 1080 x 1080 px

2) Image > Canvas Size command 1080 x 1080 px with black extension colour (presuming flattened file input)

You may also need to add a save as step if you require different settings or formats.

The Droplet settings will depend on your workflow, I am guessing that the action steps are the sticking point? More on Droplets/Batch here:

https://helpx.adobe.com/photoshop/using/processing-batch-files.html

When recording the action, start with a larger image than 1080 px.

Stop recording after recording the fit image step. 

Setup a canvas that is not 1080 x 1080 px.

Start recording again, then resize the canvas to 1080 x 1080 px, stop recording.

This is not a linear recording, you need to prime the action steps from different sized images, so that the recording and then playback works as required as a linear process on the final images.

Hope this makes sense.

If you are not working on flattened images, or a mixture of flattened and layered images then the process is different but similar.