Hi Greg,
There's probably a few things going on. The server account that you login with via SSH may be different from the account that PHP and/or Apache runs as, and they all can have different default timezone settings.
We let users specify the timezone under Admin > Settings > Regional Settings > Timezone Name. What this does is set PHP's default timezone with the date_default_timezone_set() function. This affects the date returned when you call PHP's date function.
Having a quick look at the Amazon SMS code it doesn't look like we're sending a timezone identifier. I suspect that if Amazon supported us sending a timezone as well that would resolve everything. Without that you'd need to connect to an amazon server that was in the same timezone as you or it's going to think your time is off.
Hope that helps, we'll take a look into this further and see if there's a patch we can add to resolve it.
Hope that helps!
Dave Edis - Senior Developer
interactivetools.com