In your case custom-map.css is overriden by my common.css
Try to create your own css file. Add your styles there and in map details on "Advanced options" add line into "Additional CSS style files for loading" with path to your file.
In this case after my styles will be loaded your file and it will override my styles.
I can see the same order of css files, but I can't correct explain why custom-maps.css is not override.
I can see your first map displayed by plugin call, and map div is not "OMapsID" - this div defined in my css file to disable max-width (and you set not default map CSS class), therefore my css is not set img tag.
And the second map displayed by module, and it has div OMapsID, which take my styles and you got wrong style.
I'm not well in CSS overrides, I though it have to be correct work.
I suggest to check
1 - in your custom-maps file add override to definite map div, like
max-width: 100% !important;
Probably in this case direct override (not by class) will do what you want
2 - you can create Custom HTML module, publish it instead map module, and call there plugin