A documenatry on alexander the great that I found on youtube said that Alexander paused his campaign in the east for a year to go back to egypt, where he 'founded' alexandria. In like, a year, then he went back to campaigning in the east and later died of drunkeness or malaria (or whatever).
But what actually went on, or what do you suppose went on (if we don't really know for sure what went on)?
Alexander established Alexandria in 332/331 BC but, like most of the settlements he founded, he did not remain in the region long enough to oversee its construction. Even so, in the case of Alexandria it seems he had a strong interest in the proper development of the city. Arrian tells us that "a sudden passion for the project seized him" (3.1.5) and that he drew up detailed plans for the architects to follow in its construction. He set out where the marketplace was to be built, the location of new temples, and where the city walls were to stand.
But you're right when you mention that he left Egypt to continue his campaign. According to Arrian, he left his new city to visit the shrine of Zeus Ammon, proceeding afterwards to the city of Memphis and leaving Egypt by Spring of 331. Therefore the actual construction of Alexandria was managed by the officials he left to govern the region. Chief among these men was Cleomenes, a cruel and abusive man who ruled Egypt until Alexander died in 323. The exact details of the city's development under his reign are unclear but anecdotes have survived. The Oeconomica, a treatise on economics attributed to Aristotle, relates that Cleomenes attempted to evict some locals to provide land for the new city but they bribed him in order to let them stay. Later on, when, according to Aristotle, the city was completed he came back and evicted them anyway when they couldn't afford a more exorbitant pay-off. This suggests that the key parts of the city were built before Alexander died as Cleomenes did not long survive the king's death. It also suggests that Cleomenes had carried out the construction using some heavy-handed methods.
Alexandria would go on to become an important cultural center within the Hellenistic world. This was under the rule of the Ptolemaic family, Cleomenes' successors. After Alexander died the province of Egypt was given to an officer named Ptolemy, a man who founded a dynasty that ruled Egypt for nearly 300 years. In 321 Ptolemy illegally diverted Alexander's funeral procession and gave the king a splendid burial in Alexandria. This suggests that the city was in good enough shape by then to receive such an honor. However it is worth noting that not all sources agree on this though. One says he was originally entombed in Memphis.
Simply put, Alexander may have formally founded Alexandria but the city's construction was handled by his appointees, in what was probably often a less than friendly way. Furthermore, the city's development into what some call the ancient Versailles was a process that long outlasted him.