Inspecting the button with Firebug shows:
<input type="submit" class="btn button hikashop_cart_input_button art-button" name="add" value="Add to cart" onclick="var field=document.getElementById('hikashop_product_quantity_field_1');if(hikashopCheckChangeForm('item','hikashop_product_form')){ return hikashopModifyQuantity('405',field,1,'hikashop_product_form','cart'); } else { return false; }" style="zoom: 1;"/>
405 is the correct product code. If I remove the Accessories tab, the product is added correctly.