Piotr, This appears to be classic behavior when you have a mismatch between your calendar worktimes and the default hours per day setting. In Project, all durations are stored in minutes. Any time you enter a duration in “days”, Project will automatically translate that value into minutes using the hours-per-day setting (x60 minutes/hour). Under default conditions, your 1-day task takes 8 working hours to complete, but if you have shortened your standard workday from 8 hours to 7 hours, then your “1-day” task beginning on the early morning of 03-Jan will spill-over 1 hour into 04-Jan. The situation is complicated if you have manually entered any dates at all, since the default workday start and finish times may not match your calendars.
Go to settings and choose a date format that displays the time of day. Then all should become clear.