Well, if you look at the introduction of Webster's 1824 Speller, you will find that phonograms are taught the same way O-G, Spalding type programs teach them. From the looks of it, Webster taught all the sounds of each phonogram. He also had the Syllabary that taught long (ba, be, bi, bo, bu) and short syllables (ab, eb, ib, ob, ub) before beginning 3-letter words and working toward multisyllable words in a systematic way. All of which dc had to learn to spell and read at the same time.
What I'm trying to say is that the author of that program could have very well done her research and based it off that research which ended up looking a lot like Spalding type programs. I guess I'd give her the benefit of the doubt :)