Within the fae there are those with the ability to travel through time, which isn't used as much as it could be due to worries about how their presence might affect the time they're visiting. However there have been times when certain groups have used this ability to their advantage.
Time travelling, generally, isn't dangerous, but it can be if the user doesn't have a good understanding of the magic they're working with. This becomes more of a problem on Earth when the fae arrive, because some of the mixed-bloods begin their studies but leave before they are completed which leads to an incomplete understanding of the magic and other never find the school but realise that they have the ability to travel through time. Willow, the Queen at the time of the fae's arrival, does her best to make sure that as many people as possible are trained, even though the majority of the elders do what they do best - bury their heads in the sand.
The thirteen families also have time travellers within their midst, which has more of an effect on Aerith than it does the whole web. Aerith becomes the home of a large group of time travellers, who do their best to affect the world so it become the way they want it to, even though this is much harder than it seems to be. They have their rules, but people often break them, which also affects Aerith.
Some of natural doors around the web can also send someone travelling through time. The majority of travellers don't even know that's what happened to them, because it's not normally the long term doors so they often assume that they'll never get back home anyway and do their best to make a new life wherever they are.