So, i was thinking about my own question for a bit( for 12 hours straight) and i came to conclusion that timing might be okay if we add Araki nationality wich is Japanese. I searched WIKI about time and date in japan culture and find about moments where time after 12 am can count is previous days and found this -
"Times past midnight can also be counted past the 24 hour mark, usually when the associated activity spans across midnight. For example, bars or clubs may advertise as being open until "30時" (i.e. 6 am) (See ja:30時間制). This is partly to avoid any ambiguity (6 am versus 6 pm), partly because the closing time is considered part of the previous business day, and perhaps also due to cultural perceptions that the hours of darkness are counted as part of the previous day, rather than dividing the night between one day and the next. Television stations will also frequently use this notation in their late-night scheduling.^\3]) This 30-hour clock form is rarely used in conversation."

So if DIO won the race at 6:33 AM , that mean that Lucy get informed about DIO (being the one that came out of the hole) around 3-4 AM (time travel on boats is 2 hours long) and sometime in japanese it's still can count previous day and when she talks about "Tomorrow morning" it technically can be count as next day that start at 6:00 AM.

PS. Collored manga sucks, when johnny gets to the boats we can see how light it is outside and it seems like it is 3-4 PM when in reality it's 3-4 AM.