Indonesia and other -sia words

Ihn-doe-knee-jzuh or Ihn-doe-knee-see-uh?

I've noticed that British people seem to pronounce it as the latter. I pronounce it as the former, and I noticed that it was difficult for me to decide how to write the final consonant. It's a combination of j, sh, and z. You can hear it here: http://www.merriam-webster.com/cgi-bin/audio.pl?ggindo02.wav=Indonesia
They record it as "zhə".

Does this sound not exist in British English? Is that why they pronounce -sia as see-uh?

It's just a dialect thing. Americans tend to use "zha" and Brits use "see-ah". It's not that the British can't say "zh" sounds -- they have that very sound in "treasure" and "leisure" and many other words. It's just a preference, and the way they grew up hearing and saying "Indonesia".