It's your world, and there is certainly no reason why an alien world would have the exact same year and day length as ours or would have months and weeks etc of exactly the same length, or why they'd have a day divided into two 12 "hour" segments. I've read fantasy where they use words like marks, bells, glasses, ticks, clicks, beats etc. as names for units of time that are roughly equivalent to ours. I've also read books where there are glossaries that name the months, moons or days etc. Same for units of measure that are appreciably different from real world ones (like feet, yards, inches, pounds etc). Some readers like this approach while others dislike it. I'm not sure whether changing the word for things like "seasons" makes sense or not.
But it's not unreasonable to just "translate" the units of time and distance into the closest applicable ones for our world, just as other words and concepts are "translated."
I always scratch my head, though, when people comment that shorter units of time (aka minutes and seconds) are something that didn't exist until mechanical clocks with second hands were invented.
Actually, time measuring devices go back a long way, and the concept of the second is pretty old. It was first defined as as 1/86,400 of a mean solar day in 1000 BC (this definition lasted until 1960). And the Babylonians actually were the ones who came up with the idea of subdividing time units into 1/60 of 1/60 of 1/60.
The first mechanical clock with a second hand appeared in the late 16th century, but that doesn't mean the concept of a second didn't exist before then or that people needed watches with second hands to conceptualize or roughly estimate the passage of short time units.
Some links about time in case anyone is interested:
http://en.wikipedia.org/wiki/Second
http://en.wikipedia.org/wiki/Unit_of_time
And this one covers the history of many types of timekeeping devices.
http://nrich.maths.org/6070