Another questionable pronunciation. In the Italian peninsula, syllables "sci" and "sce" are traditionally pronounced "shee" and "sh-EH". It's "sca", "sco" and "scu" that are pronounced "ska", "sko" and "sku". As I said in a previous thread, since we have no sure way to know what Latin really sounded like, it's the Italian pronunciations that should be followed.
While true, we don't have tape recordings of classical Latin being spoken, and so cannot exactly know what it sounded like, we can know with reasonable confidence what classical Latin sounded like based on reconstructions from daughter languages, misspellings, contemporary pronunciation commentaries, and other sources. Those reconstructions are what you will typically find in Wiktionary entries for Latin words, often alongside an ecclesiastical pronunciation. The ecclesiastical Latin pronunciation which you describe is fine, but it's simply not what's being taught in this course, so you should not expect to find it in the course recordings.
As a side note, reconstructions of Latin are likely to be more accurate than reconstructions of just about any other language of comparable antiquity because of the relative abundance of all 3 of the sources of evidence which I mentioned above, especially the daughter languages.