Here is another site that has pronunciation by native speakers: http://www.forvo.com/search-tr/ben%20yerim%20ben%20i%c3%a7erim/
You are not crazy. However, the pronunciation of the TTS is not perfect. Also when people speak quickly, I wonder if it sounds slightly different. The language is phonetic. Once you learn the Turkish sounds for each letter, they will be used every time you see that letter. Are you thinking of the English sounds for those letters. https://www.duolingo.com/comment/7702767 http://www.forvo.com/search-tr/ben%20yerim%20ben%20i%c3%a7erim/
I too am waiting to hear if vowel reduction is involved?
What are the subject conjugation for eat? I eat you eat He/she/it eats we eat you eat they eat?