You use multiple taxonomies at once, so use'relation' => 'AND'
:
<?php
$args = array(
'posts_per_page' => -1,
'post_type' => 'products',
'post_status' => 'publish',
'tax_query' => array(
'relation' => 'AND', // this is what was missing
array(
'taxonomy' => 'subjects',
'field' => 'name',
'terms' => $shortcode_atts['subject'],
),
array(
'taxonomy' => 'plans',
'field' => 'name',
'terms' => $shortcode_atts['plan'],
),
),
);