Why time functions show invalid time zone when using ‘c’ time format?

The issue is that for correct output WP needs to process date through date_i18n() function. When you use date format, hardcoded in PHP code (not simply saved in PHP DATE_* constant) like 'c' – it’s not available to your code and so for WP to process.

System-wide fix would be to re-process date with analogous format that can be accessed by WP code:

add_filter( 'date_i18n', 'fix_c_time_format', 10, 4 );

function fix_c_time_format( $date, $format, $timestamp, $gmt ) {

    if ( 'c' == $format )
        $date = date_i18n( DATE_ISO8601, $timestamp, $gmt );

    return $date;
}