Although this model has been diagrammed a handful of times on the internet, there are only a few published sources that I have found, and all of them trace back to Gay Merrill Gross’ “Origami: New Ideas for Paperfolding” (1990), which lists it as a traditional model contributed by Dorothy Kaplan. I emailed both of them to ask about the model; Dorothy says she learned the model in 1980 from a Thai woman, during an origami workshop at Brookdale Community College. To my knowledge, the model does not appear in any reliable source material about Japanese or European folding traditions, so the model probably did originate in Southeast Asia. A story that Gay told me gives further evidence for this conclusion:
When I showed the model to Toshie Takahama of Japan when she visited our convention in the late 1980’s, she said that she had not seen it before. […] So my feeling about the model is that its origin is traditional Asian but not Japanese.
Update 14 March 2012: the Thai Tulip also appears in “Origami Flowers and Flower Arrangements” by Joan Appel and Alice Gray, 1983.
The accompanying stem also deserves some attention– “Origami: New Ideas for Paperfolding” attributes the model to Mitsunobu Sonobe, but the NOA’s “Origami Textbook” lists Kunihiko Kasahara as the creator, and several other reputable sources, including John Montroll’s “Easy Origami”, either do not specify a creator, or label it as a traditional model. Given the extreme simplicity of the model, it is quite likely that it has been invented independently, several times. This sort of situation is more common in geometric origami, and the solution I’ve seen most often is what I’d refer to as the multiple-creators doctrine: if a model is either exceedingly simple or an obvious consequence of some well-known process or property, AND there is sufficient evidence that it has been independently created by multiple authors, then the model may be considered to be traditional. The origami tessellations community is where I’ve seen this concept used most often, but I think it applies equally well outside of that genre.