Everytime I hear a native speaker say 'province', I notice -vin- is pronounced as more like vən than 'vin' as in the car's VIN number.
province?????_??_???????
Does it sound odd for you to hear pro-VIN-ce instead of pro-vən-ce?
AME -- ˈprɑːvəns
BrE -- ˈprɒvɪns
Since the page is in Chinese, I haven't been able to find the voice sample you referred to.
I would like to invite you to view and listen to this youtube clip:
YouTube - China 2010 Earthquake 1 of 2 and Global Update - BBC World News 40th second and on, another at 2:20
The British newscaster and reporter sound pronouncing 'prinvince' --the vin part as [vən] as well.
However, if you continue viewing it, you can indeed find another reporter pronounce it closer to pro-vin-ce than to pro-vən-ce.
Both, if I heard correctly, sounded like 'prɒvəns.
For unstressed short i sound at the end of the word, it is not uncommon to pronounce like 'uh', especially the "in" sound. I've heard people saying both ways. To me, they're all correct.