conditional statement for custom taxonomy

I’m pretty sure you shouldn’t use negation in your conditions… If you check ! is_tax... it will be true not only for other taxonomy pages, but also for singular pages, and any other…

So it should look like this:

<?php if ( is_tax('taxonomy-name','taxonomy-one' ) ) {?>
    <div class="test" style="color: red"><?php the_field('field_name'); ?></div>
<?php } elseif ( is_tax('taxonomy-name','taxonomy-two' ) ) {?>
    <div class="test" style="color: green"><?php the_field('field_name'); ?></div>
<?php } ?>

And about lack of documentation… I have no idea where have you looked for, but there is codex page for is_tax: http://codex.wordpress.org/Function_Reference/is_tax 😉

PS. If you want to check if given post is assigned to term, then you should use has_term function.