I just listened to a few sample sentences, but it sounds like they've gone for an ecclesiastical/Italianate, rather than classical/restored pronunciation. In fact, I wouldn't be surprised if they are just using their Italian pronunciation for both languages, because that's essentially what the ecclesiastical pronunciation is.
Frankly, I don't think it's a bad idea, since there remain disagreements over what constitutes correct restored pronunciation.
Edit: After a little more listening, I can tell it's not perfectly ecclesiastical either. Namely, Google maintains the hard "t" in words like "patientia," when an ecclesiastical pronuncitaion would have it more like "patsientsia."
Horae quidem cedunt et dies et menses et anni, nec praeteritum tempus umquam revertitur nec quid sequatur sciri potest. Quod cuique temporis ad vivendum datur, eo debet esse contentus. --Cicero, De Senectute