How to use WordPress Conditional Tags in get_posts foreach loop

I’m not sure I fully understand your question, but I wonder if you mean:

if( 5 == $post->ID 
    || 'archive' === mb_strtolower( $post->post_title ) 
    || 'archive' === $post->post_name )
{
    echo 'Show me';
}

when you generate the HTML for the tabs.

ps: If you check the source of is_page() you will see that it returns $wp_query->is_page( $page ), where it uses the global $wp_query object. So it’s mainly used for main queries but not sub queries.