I'm confused about this word. It seems like it is written in kana as 「てんいん」 but when I hear it actually pronounced it sounds more like 「ていん」, as in 「ていんさん」.
The "correct" pronunciation is てんいん, but the ん sound often vanishes before い (and sometimes え). It's not that the n sound is hard to hear with your non-Japanese ears, but that many native speakers actually pronounce 店員 without the n sound at all.
|全員||ぜんいん||ぜえいん / ぜいいん|
|原因||げんいん||げえいん / げいいん|
|店員 / 転院||てんいん||てえいん / ていいん|
According to this survey (PDF, in Japanese), the majority of young native speakers pronounce 全員 as ぜえいん, and many university students are even unaware that 店員 and 定員 have to be pronounced differently.
Some native speakers wrongly remember the kana spelling of 店員, and thus 定員さん is one of the most common misuses of kanji that happens every few minutes on Twitter (see this search result). My IME can convert ぜいいん to 全員, etc.
I think you can think of this phenomenon as a set of exceptions that are not yet recognized by dictionaries but are common in reality. A similar phenomenon does not happen with relatively uncommon words like 班員 and 音韻 (as far as I know, they are never pronounced like はいいん or おおいん/おいいん).
Also note that the second kana is elongated, so 定員さん can be てえいんさん or ていいんさん, but not ていんさん or てえんさん.
The actual value of ん depends on the following sound according to the following sources.
In 店員, ん is followed by a vowel い, so the ten is pronounced as a nasal vowel /tẽ/. That's probably why you don't hear a distinct ん.