How the first visibility of Moon happens: every day Sun moves on the sky from east to west , and in end of Hijri month Moon is located a little westward from Sun, in northern hemisphere: for example, see Moon at 2015-09-11 (1436 Thul-Qedah 27): (this and other images are screenshots of Stellarium). and in some day Sun catch up with Moon and they are located on one vertical line with another, this is very short period, ( and at that time Moon is not visible, because its crescent is very small) and then Moon goes to left , i.e. to east side of Sun: for example, Moon at 2015-09-14 (1436 Thul-Qedah 30): . (So, Moon moves slower than Sun, on the hemisphere/visible sky).
At end of month Moon is not visible at day and not visible at night and not visible at sunset because Moon sets earlier than Sun, and at end of month Moon rises earlier than Sun and can be visible just before sunrise: for example, see sunrise at 2015-09-12 (1436 Thul-Qedah 28) .
At beginning of new month Moon also is not visible at day and not visible at night, but visible at just before sunset, because Sun sets earlier than Moon: for example, see sunset at 2015-09-14 (1436 end of Thul-Qedah 30 / beginning of Thul-Hijjah 1): , and at beginning of new month Moon is not visible at sunrise, because Sun rises earlier than Moon.
at beginning of new month, when moon is visible first time, it is visible only for several minutes.
for example, how long it is visible after sunset at september 14 at my location: it sets nearly after 15 minutes after sun. i have watched/checked it with stellarium . and at sunset of september 13 sun sets later than moon, even though moon is a little eastward from sun, because sun is a little upward from moon and moon sets earlier than sun.
when moon becomes visible, or visible by calculation, if there are clouds, first time, i think, it may be at any place of earth, randomly. what happens then: as spot of sunshine moves from east to west on surface of earth, as sun moves from east to west, the sunset band/stripe moves together with the spot, as it is an edge of the spot. so, new hijri date appears at this band, and, as sunset goes more and more to west, more and more people can see new moon at that places, so new date, new month zone grows westward.
so, if you are located eastward from international new moon, you cannot use it.
but, i think, if you are eastward and more north from the new moon seeing location and it is summer at northern hemisphere, and if sun is at same or less degrees below horizon for you, than at location of first seeing of new moon, you can use that first moon seeing. (this rule should be edited to be written more generally).
in your example india is located east from dubai, (and their time zones differ more than a hour), so you cannot use dubai new moon in india.
i have checked position of moon at southern hemisphere at evening of september 13 at nearly same meridian with my location, and moon is located upper than sun, and sun sets earlier than moon. so moon may be visible. should not that time be used by me, if it was visible there? - i think, if i was more east from sunshine spot, then not, but if i was on sunshine spot or on its edge of sunset, then yes, even if i did not see moon in my location, because, days are counted by sunshine spot moving, not by moon visibility area moving, and if i know that somebody somewhere in this same evening at same time has seen the moon, i (am going to) use it. i have checked it once more and i see that moon was less than 3 degrees upper than sun at evening of september 13, 2015, near madagaskar (ie nearly at utc+3 zone as me, but in southern hemisphere of earth). as i know, 3 degree of distance is not counted as distance at which moon can be visible, for example, see moon visibility maps here: http://moonsighting.com/1436zhj.html .
i have found a paper written almost a year before my answer, suggesting similar method. but he suggest to use meridian, not sunset line. i compare these methods:
in this images, 1st one is for sunset line method, and 2nd for meridian method, new moon appears at the central dot. difference is only in the 2 points shown with pink circles. shades of gray mean areas of twilight after sunset. 1 mean 1st day of new month is started, 30 means last day of previous month is started on these points. what people are expected to think at the differing points? in the sunset method, people in the upper right point think "we are at same sunset, so let's start new month, even if new moon is not visible here", in the lower central point: "sunset was some time ago here, and, only now, new moon has become visible, in the same meridian with us. they has similar local clock time with us, but that is not important, sunset is passed here, and last day of the last month has already started". in the meridian method people think: upper right: "sunset has just passed, new moon was just now seen in the same sunset line, but we are on the easter meridian compared to them, so... earth has rotated over our clock zone... so... but we decide to not start new month", lower central: "we are on the same meridian with the people who have seen new moon, sunset have passed some time ago, but let's start new month with this evening". i think, the sunset line method is more logical, correct.