The article seems to be sorely lacking in details, and when it finally does mention the specific models, it seems that they only actually tried to get inflation out of toroidally compactified Type IIa String Theory, claiming that this was generic. If anything, this is the opposite of a generic situation. Toroidal compactifications preserve far too much supersymmetry to be generic, and as the article mentions, there are other reasons to expect that inflation won't be visible in the IIa theory. Additionally, the article fails to mention that there are a number of inflationary mechanisms in string theory that seem to be quite generic. Included in these are KKLT, KKLMMT, Brane Inflation, DBI Inflation, and many more stringy inflation models which I haven't mentioned. In fact, if anything, the problem currently seems to be that there are too many viable inflationary models in string theory.