the TimeSlider is just used to pick a StartDate and EndDate which we refer to in the API as a TimeExtent. The TimeSlider is usually bound to the Map.TimeExtent property, when the user interacts with the TimeSlider it changes the TimeExtent property on the Map. when the TimeExtent property of the map changes it loops through its layer collection looking for layer types that support time data. If it finds a layer type that is TimeAware then it will request the data from the service and pass along the time values so that the returning data matches the TimeExtent. There could be caching in two places, caching can be occuring on the REST service, when the REST service see url that is identical to a request that it recently repsonded to, then it will pull it from cache to be more preforment, The second place you have caching is in the browser, if the browser sees a url that is identical to one it has already responded to it will return the cached response.
One more thing to note is there is a limit on how many features will return from the server, I believe the limit is 1,000 features for a single service request for ArcGIS Server v10. It was only 500 features in v9.3. So if there are 10,000 features your only getting 1,000 of those features. So If you are using the TimeSlider and requesting a small date range you may get back 500 features, but then you increase the range which is valid for 1,500 features, but only 1,000 features will come back. Hope this information helps.