It's pronounced [c̟ɕiʑimete], although in careful speech it would probably be [c̟ɕiɟʑimete]―there's no contrast between [ʑi] and [ɟʑi] in Modern Japanese, so the word will be understood either way.
For the pronunciation of ち and ぢ, see section 4.3 "Affricates" in Vance's The Sounds of Japanese (2008), starting on page 82. Most of this section is available online at Google Books.