Short answer: no. This is not required for accessible websites, actually. But if you really need such tools (like contrast change button, or font size change button) check out plugins.
Now, to explain in more details:
What do you mean by “accessibility tools”?
In the past many accessible websites contained tools (buttons, links) for changing font size or color contrast on the website, for example. This was mostly in times when web browsers and assistive technology software were not playing well together and thus accessible websites themselves had to provide some accessibility tools for users.
Generally, these tools can be usually found somewhere on top of such website, in the header, or when clicked on a floating accessibility button, or similar.
Are these needed?
As web browsers, assistive technology software and operating systems improved, nowadays these tools are redundant when your website complies to accessibility standards. They may still make sense on a website that is not fully accessible though.
People with special needs already have their computers (operating system, web browsers and other software) preset for their needs, including high contrast and bigger fonts. Also, modern web browsers provide easy font change out of the box (usually with CTRL and + / - key combination and/or in the browser options).
As WebMan Design accessibility ready themes support the assistive technology, those accessibility tools are not required if you build your website fully accessible with these themes (mind your website content and plugins, as the theme has no control over these – check out “Accessibility” section in your theme’s documentation).
→ Test your website accessibility
But I still want/need those tools!
Sure, if you still need to use such accessibility tools, please feel free to add them to your website using a plugin: https://wordpress.org/plugins/tags/accessibility
You might also want to check some more info such as these video presentations from WordPress.tv: