So the "week" and the date have nothing to do with it, and the problem is to do with timezones and the fact that the same instant is referred to by different names in different timezones (which is exactly what makes different timezones different).
Since the timezone is specified (I don't think there's any ambiguity about "PDT" representing "Pacific Daylight Time"), then constructing the timestamp should take that into account. Then reformatting that timestamp for the local timezone would give the correct day.
$input_string = 'Tue 19:00 PDT';
$target = DateTime::createFromFormat('D H:i T', $input_string)
echo $target->format('l, Y-m-d H:i:s');
Or are you saying that the week is wrong in the result? If so, NogDog's questions haven't been answered (I'd sum up most of them by asking "what do you mean by 'this week'?" I can think of at least four different definitions even without considering timezones).