Hey,
Sorry - I actually replied to the wrong thread - that was suppose to go in the cookies thread! Anyway - I'm havng a look at your server. session_cache_limiter is set to nocache which is fine.
I don't understand what you mean by it "doesn't time shift" with regular date command? Obviously if you use date() on it's own it won't do the time offset command which makes the forum time correct for individual users. I notice that your server time is slightly out anyway (It says 54 minutes now and it's actually 48 minutes so the server is some 6 minutes out).
You said you changed host recently. Did you take into account the fact that the host may not be in the same country as the old one? The new host looks like it's in Europe, so will be on a different time setup, you'd need to offset it in the admin settings.
I'll keep checking the server to see if the time "changes" over the next few hours.
Grudge