Author Ambrose Bierce uses several narrative shifts to convey the various emotional states that his protagonist, Peyton Farquar, undergoes in "An Occurrence at Owl Creek Bridge." He begins in a straight forward third-person narration in Part I, and continues this form in Part II; however, there are some revelations about what Farquar is actually thinking in the second section. In Part III, Bierce shifts to what can best be described as a modified first-person narrative, in which part of the story is told from an omniscient narrator, and part comes from Farquar himself. The final shift in the last two paragraphs, back to a third-person narrative, is meant to serve two purposes. First, in the next-to-last paragraph, it is meant to confuse the reader, much in the same way that Farquar is disoriented from his experience. Secondly, it shows that Farquar's life has ended--he is dead and can no longer describe the action from a first-person perspective.
In the previous paragraph I addressed your question as one that questioned the various narrative shifts (from third-person to first-person and back again), rather than as the tenses used (from past to present tense). Now, about the tenses, Bierce apparently wanted the next to last paragraph to show that Farquar is still alive, but barely--the things he describes are his final, fleeting thoughts during his last second(s) of life, between the time he falls between the railroad planks until his neck snaps or he suffocates. The final paragraph reverts back to past tense, for he is now dead.