There is a tradition of transcription which treats all syllabic sonorants in English as deriving from schwa plus sonorant sequences, and that is a phonologically credible analysis. The tradition that transcribes syllabic [n] as [ən] is basically using a broader transcription than the one transcribing this as [n̩]. There is actually phonological evidence that schwa is deleted, coming from an allophonic rule where /t/ becomes [ʔ] immediately before [n, n̩], but not before schwa. You see this in "lighten" ([laɪʔn̩]) but not "light a newspaper" ([laɪɾənuʊs....]). This shows that /t/ and the nasal are phonologically adjacent, thus there is no phonetic schwa after the glottal stop (thus supporting the syllabic sonorant transcription).
The problem is that for something like "seven", there is a brief period between the release of the fricative and moment when lingual closure is made, where there is something that could be called a schwa-like vowel. There is no definitive test that will tell you whether that moment is "a vowel" or simply a transition between a consonant and a syllabic nasal. The same goes for "problem".
In the case of the initial syllable of "employee", I would say that is unambiguously [ɛm...], not even schwa, but that is no doubt a dialect difference, and I can imagine there are dialects with reduction. If you switch to "employ", I can pronounce that [ɛmploɪ] or [m̩ploɪ] (not particularly natural, but not totally out), so reduction to syllabic nasal is optional for me, word initially. In that context, you don't get *[əmploɪ]. This argues that the apparent schwa-like vowel is just a release feature, and there actually is a rule reducing schwa plus sonorant to a syllabic sonorant (obligatory for me; reduction to schwa is what is optional, for me).
It is very hard for students to believe instructors telling them that there is a schwa, or that there isn't a schwa, when the student's own pronunciation is different. I am a fairly aggressive reducer, and I found that some students had syllabic sonorants (thus agreed with me) and others had schwa plus sonorant (thus disagreed with me, and some of their colleagues).