I hear 进, but a better answer is probably that the sound could only possibly be "jin" because there are no characters pronounced "zhin", which means Chinese speakers have a bit of leeway as to how clearly to enunciate in practice....
If this doesn't make sense, look at our dictionary and compare the "zh" and "j" entries (use the "browse by initial" menu on the right). A quick look will show that Chinese has evolved in a way that makes the distinction I think you are talking about irrelevant in practice. So we have "jia" but not "zhia" and "jiu" but no "zhiu", etc.:http://popupchinese.com/dictionary
The one exception would seem to be the finals that start with the vowel u (i.e. ju and zhu, juan and zhuan, etc. ) but even this isn't phonetic overlap so much as just laziness in the pinyin standard. The "u" which follows "j" is pronounced like the vowel-sound "ü" in lü or 绿 (i.e. with umlaut) whereas the "u" which follows "zh" is pronounced like the vowel sound "u" as in lu or 路 (no umlaut).