Here are few tips for GM how to handle fantasy terms of time. In fantasy games months, weekdays and even hours and minutes might have different names than in our real world. It gives some detail in setting, but I also see some problems in it. They do give detail to setting, but is it necessary for players to learn this new time system to keep track on "what time it is"?
Years are basically simple. As it is fantasy, you cannot compare time line to ours. So in fantasy setting it could be year 2300 but they don't fly with space ships as it cannot be compared to our time line. Also I think that in fantasy settings years are count from something important. Like 230 years after King Diamond. 500 years before The Plague and so on.
In some games it is more important to know what year it is to know what kind of the setting is in that time period. Example is Middle-Earth. But for some games it doesn't matter for players if it is year 300 or 500 if there is not that much detailed history or GM doesn't want to put game in specific place in time line what differs radically from default setting.
Also you should note national differences. Orc nation doesn't care do they live year 150 after King Great of White Reign was crowned, but they might live year 1400 of Orc Awesomeness. Little detail what might confuse a game. Basically it is easier to use this default time. (In real world Jews live in different year than "we").
If fantasy setting uses 12 month years it is easy and logical to track days. Still, if months have different names that we are used to, it might be a bit unclear for players what season it is currently. If GM just announces, that "it is third day of the month of the three diamond stars" players who aren't familiar with setting's calendar might be confused. And then GM must explain: "well, it's kinda like our March."
It is easier for GM to say "it is third day of the THIRD month of the three diamond stars". This way players hear the fantasy setting month name but also hear which month it actually is they can compare it to.
But if there are more or lass than twelve months in a year, it get's a bit complicated as there is not enough or there is more months to compare. But it can be easy still. Instead of saying "month of the golden moth" you can add: "EARLY AUTUMN month of the golden moth." That also explains directly what season the month is in.
I don't think GM should convert strange setting months to our months, but when telling what month it is currently GM can also tell in what season and place of the year the month is located. That saves a bit of time and confusion, as GM doesn't have to explain when that fantasy month is.
Seven days per week, more or less? It actually doesn't matter that much. Week as we know it is usually work from Monday to Friday, rest in Saturday. In fantasy setting usually people work every day of the week. There might be "holydays" what are free, but otherwise weekdays are a bit different than ours. Players should know how many days there are in a week, but should they know what they are called? Not necessarily. Same as with months. Instead saying it's Gorkaday, you could say "it's fifth day of the week, Gorkaday". Players can keep track of time knowing which day it is instead of just a name. Weekdays are easy to learn I suppose, so if players start to remember them, GM can drop the ordinal number out.
Hours, Minutes, Seconds
How many hours there are in a day? That's easy to learn. GM can go the easy way and just say how many hours it takes to travel, how many minutes some action takes or how many seconds character has time to react. It helps the game a lot. But if GM wants to put setting fluff for example when NPC is talking, he can use suggestion of times from his rulesbook. If one hour is one hourglass, then 45 minutes is three quarters of a hourglass. That should be easy to understand and remember. I mean, it is a HOURglass. Second might be a blink of an eye. And so on. But to make game faster, it's just easier to say that it is five hours away than: "to travel there, it takes the time to turn hourglass five hours around". Little detail, but is it necessary?
Also in combat situations minutes and seconds are way much easier to handle than setting specific times. Basically fights are using rules and dice what aren't in game world (characters don't roll dice against orc bandits to see who wins) so to make combat easier to comprehend, use times easy to comprehend.
With little setting details you can make fantasy world more realistic and living, but don't make gaming too complicated. If you describe something in setting terms and have to repeat it in our world terms, I think the effect is partially lost. Hide our world terms or explanations in your setting terms.
"Prophecy tells: After seven moons, Shabanday -the seventh day of the week- the dark lord will rise again."