http://www4.ncsu.edu/~nwsfo/storage/cases/20010614/
And here is a quote from the site:
"Allison was the first tropical cyclone of the Atlantic Hurricane season. Allison's origin can be traced back to a tropical wave moving across the Caribbean in late May. The disturbance moved into central America and remained relatively stationary for several days before moving into the southwestern Gulf of Mexico in early June."
Basically it looks like Allison's wave moved into Central America, and sat there (may be meeting up with Mexican moisture), then moved into the SW Gulf/BOC and then moved north becoming a TS.