The trainer aims for an Israeli modern Hebrew, Ashkenazi dialect. Ayin shows up as a glottal stop in that dialect (שִׁיוּר and שִׁיעוּר are distinct and used as minimal pair tests in the pronunciation trainer, for instance), but there isn't a distinction between Ayin and Aleph. Learning this should make you sound like an average Israeli (and the recordings that the trainer utilizes are all made by Ashkenazi Israelis).
Note: As of September 12th 2019, we no longer provide official support for our Anki based pronunciation trainers and word lists. You are more than welcome to still purchase and use them, but the support we are able to offer for these products is limited. For supported languages, these materials are already built into the Fluent Forever app.