Turn on the display of time in File > Options, General. For the tasks that are beginning in the same day as the predecessor finishes, does the predecessor begin at the start of the business day but end before the end of the working time set either for the Project or for the assigned resource?

Tell us a bit more about:

• How many working hours are in a day - set in Change Working time
• Do you have resources assigned with different working time calendars?
• What is your definition of "day" in File > Options, Schedule?