... perhaps it is telling: I can't figure out if you are being sarcastic or not. :/

In my head I keep a concept of "physical day" (real calendar days, followed by other, real calendar days) and "logical day", which is the day as I am currently experiencing or referring to it. If, after a long Monday, you're up past midnight (i.e, it is now Tuesday), then the "phyiscal" day is "Tuesday" and the logical day is "Monday". The logical day progresses either when you go to sleep (at which point one ends, and another begins when you wake), or at dawn.¹

Person to person speech is almost always in logical days; "tomorrow" would not be a minute past midnight in this system. This at least makes some things make sense.

¹There _still_ tons of issues with this, such as people who work at night and sleep during the day, people can be on different logical days, some places don't have a dawn for several months…

Not sure if you're being sarcastic or not.

If I said "the servers are down for maintenance at 2am tomorrow" when would you think they will be unavailable?

I wasn't being sarcastic at all.

If you said "2am tomorrow" I would assume two hours after next midnight. Perhaps this is a result of my usually late schedule because I normally go to bed around 2am, so everything up to then and including midnight is "tonight".

If I said "talk to me about it tomorrow" and later we're chatting at 1am, are you going to think I meant now?