The amount space looks the same on my screen for both the first two links.
The second however isn't anything to do with the plugin as far as i can tell, i don't output any spans or breaks for the tabs, and only paragraphs inside the tabs.
Screenshot of mysterious paragraphs with span and breaks
My plugin's code, specifically the two functions that produce HTML output for the tabs.
I'd have to guess/assume this is something to do with what you're putting into the editor, and/or something another plugin you have installed is adding.
Could you create a test post and put the following in the editor please.
Line of text 1
[tab name="Tab name 1"]Tab 1[/tab]
[tab name="Tab name 2"]Tab 2[/tab]
Line of text 2
Save it, and provide a link to the test post please.