Tithis are Lunar Days. They do not correspond at all to Solar Days. They have nothing to do with the days we experience by the rising and setting suns in our various cities. Our current Western calendar is based on solar days. We are used to thinking in this way. The Moon however does not always rise at night, nor day, nor any time. Actually, the Lunar cycles are much more complex than that. The Sun takes much of our attention because it is so essential for life's operations. And it is so bright, you can't ignore it. The Moon is the opposite, we can fully ignore it, and hardly know where it is ever, unless it makes a bit of a showing as a full Moon or something, then we notice it's beauty. That's about it. But the Moon does have cycles which are very exact, and with modern astronomy we know exactly where it's going to be at all times. In fact, this has been known for a long time- thousands of years- more or less with rough accuracy.
So it is possible to correlate the steady movements of the Sun through the degrees of the zodiac over the year it takes for us to circle it, and simultaneously we can track the exact degrees of the Moons apparent movement through the Zodiac over that same year, and we can track their relationship. In fact, since the zodiac is a 360 degree circle, and we circle the Sun once a year, therefore we say that "the sun moves through the zodiac in a year" or "takes a year". Well, the Moon circles really fast around the earth, and when we look at it, we see it is "in a certain sign" all the time too, just like the sun, and so we can watch the Moon "move through the Zodiac too" but it only takes about 27 days to go all the way around, and has been doing this, for apparently thousands of years as we've been watching it.
So, the Moon "rips ahead" of the Sun over and over throughout the year. If you chart the too together, the Moon goes all the way around every month, catching up to the Sun and passing it over and over every 27 days. If we want a lunar month, we can take that 27 days or so that it is, and divide it into 30 sections, and 360 divided by 30 is 12, so this mean that every time the Moon gets 12 degrees ahead of the Sun as it rips ahead around the zodiac, it has moved one lunar day out of it's 30 "day" lunar month. So I just defined a system of days and a way of telling when they start and end.
When the Moon moves 12 more degrees ahead of the Sun, starting from the point of exact conjunction when they meet every 27 days, then we say the next lunar day begins. So, since it takes like less than 24 hours, well, if the two planets are conjunct by Gods choice at 2 AM on Wednesday, well then when that occurs, your clock may say 2 AM, but on the other side of the world, that FIRST TITHI of that month begins the previous or next day at a different CLOCK TIME for them. You see, the Lunar calendar is tied to TWO PLANETS interactions, and these take place WHEN THEY WANT and have nothing to do with what day it is where.
Our current calendar is particularly centered around our reality- our SOLAR DAY and night and SOLAR YEAR and so on.....a lunar calendar takes much more astronomy, math, calculation, astrology and overall intelligence to relate to...but it is much more representative of REPEATING PLANETARY patterns than the rather blunt and dumb solar calendar. The Solar Calendar is like "the calendar for the masses" and the "luni-solar or Vedic is more for real Brahmins, who are simplly more intelligent and trained". But the world uses the solar of course, and that's fine.
So, tithis actually start for the whole world at the exact same moment, but that is on a different day and time on different parts of the country or earth because we all have our clocks set relative to our sunlight day. Then there's "which day is it" so we have invented the international dateline which runs down the Pac. Ocean, and starts the new day in places like Australia- so that's why-In relation to the Earth as a whole, the SUN and MOON CONJUNCTION event in the great sky, which happens every 27 days and starts the new lunar month off, takes place for all of us at the exact same moment(taking Geocentric calculations as usually do).
So then we relate that to local clocks for the benefit of the local clock staring person who wents to know "when it happens for them" so they can follow the changes or whatever. So since "Ekadashi" is actually when the Moon is inbetween 120 and 132 degrees ahead of the Sun, and again at 300 and 312 degrees, therefore these angles actually begin and end roundly 22 hours apart, they last that long, roughly one lunar day, and they start and stop in space at totally odd times in relation to any particular day on earth. So that is why they fall at different clock times in different cities, and this is why Panchangs or Vedic calendars which give the start and stop times of these events must be calculated and printed for a locality, or be written down in Greenwich time or some such standard time frame to be translated by the reader upon need.