>Replace the user clicking a button with an automated process and it's easy to see that the CSS+HTML is what is doing the actual processing.
In which case the complete system including the "automated process" is Turing complete, but the CSS itself is not.
>Alternatively, putting a button on a computer that must be pressed to have the CPU execute an instruction and move on to the next doesn't mean that programs on this computer aren't Turing complete.
"Programs" can't be Turing complete, it's a property of computation systems. And putting the button on the computer would indeed mean it wasn't Turing complete (unless you consider the human pushing the button part of the system).