How are days counted for late night arrivals and departures?

[Captain Monday]

What day did you arrive?

• Your flight is scheduled to block in at 23:50 and arrives at the gate on time but you do not pass thru immigration until 00:30AM
• The same flight is very very late and arrives at the gate four hours late at 03:50AM

 

What day did you depart and is it overstay?

• Your flight is scheduled to depart at Sunday at 01:05AM. You check in as early as possible and pass thru immigration and security checks by 11PM on Saturday in order to enjoy time at the lounge or shopping
• What if Saturday is your last day "Permitted to Stay until" ?