Extremely red objects were identified in the early Spitzer Space Telescope observations of the bright-rimmed globule IC 1396A; they were classified as Class I protostars Class II T Tauri stars with disks based on their colors. New spectroscopic observations covering 5.5–38 μ confirm this identification. The Class I sources have extremely red continua, still rising at 38 μm, with a deep silicate absorption at 9–11 μm, weaker silicate absorption around 18 μm, and weak ice features including CO2 at 15.2 μm and H2O at 6 μm. The Class II sources have warm, luminous disks, with a silicate emission feature at 9–11 μm. Optical spectra with the Palomar Hale 200-inch telescope show the Class II sources to be actively accreting, classical T Tauri stars with bright Hα and other emission lines. The Class I sources are located within the molecular globule, while the Class II sources are more widely scattered. This suggests two phases of star formation occurred in the region, the first one leading to the Class II sources including LkHα 349a, c that are located in the center of the globule, and a very recent one (less than 100,000 yr ago) that is occurring within the globule. This second phase was likely triggered by the wind and radiation of the central O star of the IC 1396 H II region, with possible additional contributions from the outflows of LkHα 349a, c and some nearby B stars.