Twitter time instead of date?

Use the latest_tweets_render_date filter to perform your own relative date representation.

https://www.ads-software.com/plugins/latest-tweets-widget/other_notes/#Theming

Just in case anyone else wants to display the time in this format:

add_filter('latest_tweets_render_date', function( $created_at ){
    $date = DateTime::createFromFormat('D M d H:i:s O Y', $created_at );
    return sprintf( '%s ' . __( 'ago' ), human_time_diff( $date->format('U') ) );
});

Nice one. I didn’t know about the human_time_diff function in WordPress.