Whatever I know for consideration of Tithi from Panchangam is whichever Tithi falls on the sunrise, that is considered for whole the day.
For example, yesterday there was Ashtami on sunrise and Ashtami Tithi holded upto 12:50 pm, after then Navami is started. Since there was Ashtami on sunrise, Ashtami is considered for whole the day and hence there was Durgashtami on 17 Oct. 2018.
Now, talking about for today (18 Oct. 2018) there was Navami on sunrise and holding up to 3:30 pm and after then Dashami occurs. So, there should Navami be considered for whole the day. However, as we know we have celebrated Dussehara today.
Ideally, if you observe Tithi timings for tomorrow there is Dashami on sunrise and holding up to evening (6 pm). So, there should be Dashami considered for whole 19 Oct. 2018 and hence Dussehra should be celebrated tomorrow.
Then why have we celebrated Dussehra today? Isn't Dussehra the 10th day of Navaratri i.e Vijaya Dashami? So, I am bit confused regarding counting Tithi for today. I am sure there is something I'm missing. Is there anything regarding Nakshatra or other things considered for counting tithi? or what am I missing? Looking for an answer explaining justification.