If Ezekiel was deported at the very end of the year as was customary of the seventh (rather than the sixth) year, then most of his exile would have fallen in the 8th year of Nebuchadnezzar, which means year 1 of his exile would match year 8 of Nebuchadnezzar, a 7-year difference. Thus year 12, the year Jerusalem fell in the 5th month would fall in year 19, because 7 plus 12 is 19. It takes about 5 months to get word from Jerusalem to Babylon but that is with a large group, mostly on foot. A messenger riding horseback to speed news to Babylon would have taken less time. Even so Jerusalem fell in the 5th month and the 10th month of the exile of Ezekiel if he were deported at the very end of the year would allow sufficient time for word to reach Babylon, which is 4+ months.
The same fact falls automatically from the same analysis I mentioned above, that Ezekiel was exiled at the same time as Jehoiachin and that he reckoned his years from Tishri. That would mean that Jerusalem fell in the 11th year of his exile but that Ezekiel received the news in his 12th year. This is confirmed by the oracle against Tyre in Ezekiel 26:1-2, which is dated to the 11th year but which also refers to the fall of Jerusalem as having occurred (v. 2). The distance to Tyre was shorter, particularly by ship which is what probably was the case (as Tyre was an insular nation). So Tyre had time to receive the news prior to Tishri, but your reckoning has Tyre reacting to the news of Jerusalem's fall a year too early. Note again that in 40:1 Ezekiel refers to Tishri as "the beginning of the year", and he dates this particular Tishri to the 25th year of his exile in the 14th year after the fall of Jerusalem. Jerusalem fell in Ezekiel's 11th year and the end of the 1st year after its destruction occurred in Ezekiel's 12th year. The 14th year after the city's destruction spanned from August in Ezekiel's 24th year to August in Ezekiel's 25th year. Ezekiel's 25th year began in Tishri and the vision was given 10 days into his 25th year. This also fits perfectly with the biblical and rabbinical indications that the 25th year of Ezekiel was a sabbatical year and that Jerusalem fell late in a sabbatical year. If the 25th year was sabbatical, then the 11th and not the 12th would have been a sabbatical year.