You're still using register_sidebar_widget and register_widget_control -- not the newer functions. Around lines 950 and 980 in twitter-tools.php, please change the following lines as noted:
Line 950:
// OLD:
register_sidebar_widget(array(__('Twitter Tools', 'twitter-tools'), 'widgets'), 'aktt_widget');
// NEW:
wp_register_sidebar_widget( 'twitter-tools', __('Twitter Tools', 'twitter-tools'), 'aktt_widget' );
Line 980:
// OLD:
register_widget_control(array(__('Twitter Tools', 'twitter-tools'), 'widgets'), 'aktt_widget_control', 300, 100);
// NEW:
wp_register_widget_control( 'twitter-tools', __('Twitter Tools', 'twitter-tools'), 'aktt_widget_control', array( 'width' => 300 ) );