Highcharts v4.0.4 plotting local timezone - highcharts

I am plotting UTC timestamps for an particular user whose timezone I know. Each data point is in the format "2018-06-19 13:19:52.000Z" and was added to the series of points to be plotted as moment("2018-06-19 13:19:52.000Z").tz(this.tiemZone).valueOf().
When the point is plotted, it is plotted as 6/19 13:19:52, but I would like this to be plotted in the user's timezone, so something like 6/19 6:19:52.
I read that Highcharts plots in UTC, but that if I set useUTC: false (somewhere), that it would plot in the current browser's timezone, but I actually want to plot in the user's timezone, e.g. if the timezone is "Los Angeles", then the above time would be 6:19:52.
time = new window.Highcharts.setOptions({
time: {
timezone: _that.timeZone,
timezoneOffset: _that.offset
}
}, this);
return '<b>' + this.series.name + '</b><br/>' +
Highcharts.dateFormat('%m/%d %H:%M:%S',
this.x)
+ ' - ' + Highcharts.numberFormat(this.y, 2) + ' ' + toolTipUnits;
The offset I calculated after taking the moment of one of the UTC timestamps:
moment(data[0][0]).tz(this.timeZone)._offset, here is was equal to -420
I tried something the above, but the tooltip still shows the UTC time 13:19:52. Any advice?
************************ UPDATE*****************************
time = new Highcharts.setOptions({
global: {
timezone: _that.timeZone,
timezoneOffset: _that.offset
}
}, this);
return '<b>' + this.series.name + '</b><br/>' +
Highcharts.dateFormat('%m/%d %H:%M:%S', this.x)
+ ' - ' + window.Highcharts.numberFormat(this.y, 2) + ' ' + toolTipUnits;
I updated the code as shown above, and now the data point is being plotted as 6/19 20:19:52, even though I am adding -420 to the data point (this.x). Looking into this, but any idea why?

It looks to me like you're simply going in the opposite direction.
From the Highcharts API documentation, it says "positive values are west, negative values are east of UTC." If you assume 6/19 13:19:52 is UTC time, and you want 6/19 6:19:52 (seven hours west of UTC), then you'll want to set a positive number for your offset (timezoneOffset: 420). What you're doing now is setting a negative number (-420), so it's returning an offset for seven hours east of UTC.
https://api.highcharts.com/highcharts/time.timezoneOffset
I hope this is helpful for you.
(Also, can I assume that in your return code, you're using this in the tooltip formatter?)

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...,
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http://jsfiddle.net/#&togetherjs=7IfUNtFkAE
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http://jsfiddle.net/S8wzF/1/ OR http://jsfiddle.net/S8wzF/2/
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shared is not needed and thus return statement of formatter is modified accordingly.
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useHTML: true,
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}
}
Original code contains Javascript problems (Unrelated to highcharts)
The series add data incorrectly as it is inside the loop.
Put this segment of code outside "for loop".
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type: 'line',
color: '#000',
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