As someone else on here noted, the day/night cycle is important to people and not likely to be ignored just because there are other people are on a different planet with a different day/night cycle. Just like time zones on Earth: Yes, we all know that when it's noon here in Michigan, U.S., it is not noon in Tokyo, Japan. But that doesn't stop us from still getting lunch around our local noon. It's natural and convenient.
Anyway, I think that just like with time zones, people would eventually agree on some standard way to keep time, which they would then convert to and from local time as necessary.
Others have mentioned using something like Unix time, where you count seconds continuously from some convenient starting point. In the case of Unix, I think it starts from January 1, 1970, midnight UTC. So in Unix time, January 1, 2017 is somewhere around 1,451,649,600. That is, it's that many seconds past the start of the epoch. (If I bungled that calculation, sorry, but not important to the point.) Computers have functions to convert a Unix "number of seconds" to a date and time on the Gregorian calendar. You have to specify what time zone to get the correct time, and the time you get will be different for different time zones. The computer can just as easily convert to the traditional Chinese calendar or the Jewish calendar or any other calendar out there.
Maybe for local matters, people would use local time. But people who routinely talked to folks on other planets might use such a universal standard. A big catch is that ten digit numbers are hard to comprehend and work with in your head. If it's 1,532,203,201 now and you say you want to hold a meeting on 1,532,845,282, how far away is that? It's hard to grasp quickly and intuitively.
My suggestion: Deal with it with a combination of metric system prefixes and omitting high order digits when they're irrelevant.
That is, today someone might say, "Let's get together in two days to discuss this." I doubt people will ever routinely say, "Hey, let's get together in 172,800 seconds." But they well might say, "Let's get together in 170 kiloseconds". Or instead of, "This happened on January 1, 2017", I don't think people will say, "This happened at 1,451,649,600." But they might say, "This happened at 1451 megaseconds."
Today, for small time intervals we often don't specify the high-order intervals. For example, if someone says, "Let's have lunch at 11:30", I assume they mean 11:30 today. If it's June 14, 2017, no one says, "Let's have lunch on June 14, 2017 at 11:30." People could do the same thing with Unix time. If it's presently 1,542,320,822 and you say, "Let's have lunch at 390 kiloseconds, the other person would understand you to mean 1,542,390,000. That is, take the leading part higher than kiloseconds from the present time, and then replace the kiloseconds with the value given.
Implied in this is that people would come to think of time in decimal multiples of 1 second rather than minutes, hours, day, months, and years. Instead of saying, "A typical work day is 8 hours" we'd say "A typical work day is 29 kiloseconds." Instead of saying, "We got married 5 years ago" you'd say "We got married 160 megaseconds ago". Etc. And people would quickly learn to round to the powers of ten, not to whatever number of seconds the old units came out. Like where today someone might say, "This job will take several days", people using this system would NOT say, "This job will take several multiples of 86,400 seconds." They'd say, "This job will take hundreds of kiloseconds."
Of course they wouldn't necessarily use seconds since January 1, 1970 in Greenwich, England, Earth. They could choose any convenient starting point and any convenient size unit of time. Something larger than a second would probably be more convenient, and then use fractions for smaller units. Like maybe you'd use a base unit of time roughly equal to an Earth day. (Not saying it would be based on any Earth cycle, just that order of magnitude.) Then, supposing you called this unit, I don't know, a "fwac", you might say "This project will be completed in 300 fwacs", meaning not quite an Earth year from now, or "Let's call a meeting for 6 decifwacs", meaning, the time that is 0.6 fwacs into the current (whole) fwac.
Pedantic astronomers would probably insist that the size of the unit and the starting point must have something to do with the rotation of the galaxy around the core, or physicists might think it's a great idea to base it on the time it takes for some selected isotope to decay. They'd probably win, but this would be silly and pointless. It would make more sense to just pick values that are convenient for human beings to work with.