According to the press-release, the material was taken from the site in three shipments that took place in August-September 2010. The shipments contained a total of 19.7 kilograms of highly enriched uranium (HEU) and 37 kilograms of low enriched uranium (LEU). The material was transported to a "secure federal facility" about 1,000 miles away, which is most likely the Idaho National Laboratory.
The General Atomics facility hosted two research reactors - TRIGA Mark I, which operated from 1958 to 1997, and TRIGA Mark F, which operated from 1960 to 1995. According to NRC, the facility included a building with hot cells and radioactive waste tank area. NRC licence for these facilities was terminated in 2000.
The NNSA press-release seems to suggest that the current transport included only the fuel of the TRIGA Mark I reactor. However, during preparations for decommissioning, "fuel from both reactors have been placed in the TRIGA Mark F fuel storage canal," which probably suggests that all fuel was handled together. In any event, according to NRC data, spent fuel of the Mark F reactor spent fuel was also scheduled to be transfered from the site in 2010.