I appreciate the note, and if I follow what you're saying then I hope that's not the case, because the image processing shouldn't be affected by having a <figure><figcaption ></figure> tags added as it's an HTML5 standard, like <article />, etc.

Are you using the Image plugIn

and in your tinyMCEconfig file you have the plugin registered and the command line registered. Pseudo markup here:

Your CSS should go into the Text Editor there is a specific place it gets added - just like when you do formatting - this is in the documentation on line. But when you configure the Tiny in the Editor GUI, there is the option to add the classes .

There is also some custom things you can do via the config file. TinyMCE Configuration

So look at that link and then you can add this in the appropriate place - look at formatters ..

figure.image {
    display: inline-block;
    border: 1px solid gray;
    margin: 0 2px 0 1px;
    background: #f5f2f0;
}

figure.align-left {
    float: left;
}

figure.align-right {
    float: right;
}

figure.image img {
    margin: 8px 8px 0 8px;
}

figure.image figcaption {
    margin: 6px 8px 6px 8px;
    text-align: center;
}