更改时区时，DateTime时间戳不会更改

Alright so basically, I am a little confused about how the timestamp works in DateTime in PHP. I wish to make two methods that convert from a local time to UTC and vice versa.

I currently have this:

/**
 * @param \IPS\DateTime $utcDateTime The UTC datetime.
 * @param \DateTimeZone $timezone The timezone to convert the UTC time to.
 * @return \IPS\DateTime New datetime object in local datetime.
 * @throws \Exception when the UTC date is not in UTC format. (debugging purposes)
 */
public static function utcToLocal($utcDateTime, $timezone)
{
    if ($utcDateTime->getTimezone()->getName() !== "UTC") {
        throw new \Exception("Date time is not UTC!");
    }
    $time = new DateTime($utcDateTime, new \DateTimeZone("UTC"));
    $time->setTimezone($timezone);
    return $time;
}

/**
 * @param \IPS\DateTime $localDateTime A datetime configured with the the user's timezone
 * @return DateTime New datetime object in UTC format
 * @throws \Exception When given datetime is already in UTC (for debugging purposes)
 */
public static function localToUtc($localDateTime)
{
    if ($localDateTime->getTimezone()->getName() === "UTC") {
        throw new \Exception("Value is already UTC");
    }

    $time = new DateTime($localDateTime, $localDateTime->getTimezone());
    $time->setTimezone(new \DateTimeZone("UTC"));
    return $time;
}

When I debug this code, at the last line return $time in localToUtc(...) my debugger shows the correct conversions:

However, when I evaluate the expression

$localDateTime->getTimestamp() === $time->getTimestamp()

it will return true.

So I am a little confused, I just want the timestamps to change when I change the timezone. I am thinking maybe I need to work with getOffset() but I want to make sure I do it in the correct way. I'd also prefer not to use any string format tricks because I feel like that is not the correct way.