Hi Kelvin,
Some how after reading the forum at
http://forums.macnn.com/archive/index.php/t-122957.html (reading starting when gralem found out that it was outlook having a problem)
i found out that if I take the ics file and remove the ;TZID=%timezone% at the DTSTART line (like what is mentioned on the link), all the times are working.
It seems that with "time zone support" turn on in MAC ical, zimbra cannot recognize the TZID=Asia/Singapore.
Try and let me know. Maybe sunbird does not generate that portion.
Cheers,
adrian