The 1769 transit of Venus was observed and coordinated by over one hundred astronomers around the world. How did they measure time so accurately, key to the observations having any scientific value? I find little information online regarding 18th century timekeeping devices. I assume that they were mostly using clocks intended for nautical navigation, as I think those were the most accurate of the era.
Since pre-historic times, it is the motion of stars which were used to measure time. Astronomers were well-aware of their motions and their relation to time. And as far as my knowledge goes, they had angle measuring instruments similar to modern day sextants by 18th century.
If you refer to any textbook in astronomy, one of the most important things they teach is how to keep time using motion of stars. This used to be every day(or night) practice in observatories.
There were assistants in observatories to calibrate time. It was a very important job in those times. This calculation had to be accurate. You can get the importance of this practice by your question.
They couldn't carry sufficently accurate time from London with portable clocks.
But they were able to use clocks to time measure the time between the sun crossing and the transit of stars the night before and after. The absolute transit time of stars can be trivially obtained if you know the site's longitude.
If you are on land and have an observatory to hand you can use the lunar method to determine the longitude. Determining the latitude at sea needed accurate portable clocks that came a little later