well Polish has sekretarka for female secretary, but for the very high position like "Secretary of State" the female person in this position would be Sekretarz Stanu,
but with sentence like
this my sister is a secretary - moja siostra jest sekretarką
my brother is a secretary - mój brat jest sekretarzem
Well, if you hear a sound that you don't see in writing, then that does not sound correct. Once you learn how Polish is pronounced, there aren't really such surprises.
To my ear it sounds like she stops for a fraction of a second after "sekretar-", which I guess could be interpreted as adding some slight vowel, but I don't think this audio is bad in general.