I chose 'Now' as the transfer date and:
"Error! The date provided is in the past. Please enter a different date."
It must have been the time difference. It was 9:30 PM that was next day where the bank system is, so the application considered the 'Now' is for the previous day.
Anyway, it wouldn't be so difficult to have a solution for this (not to call it a "bug", even if it is one, but after all it's very minor, part of the "annoying" category). So I had to choose 'Later' and select tomorrow's date (for me) that was 'Now' for the bank system.