Skeetobite is displaying the model data from the NHC's server that their site processed. What may be confusing on the starting points is that there are two starting points on most of the images. Let's use 0Z (8PM EDT) models as an example. At that time there are early cycle models available that initialized at that time that are very quickly available, usually posted within less than an hour after that time. But at the same time there are late cycle models that were initialized 6 hours prior, at 18Z (2PM EDT). Because the models are so complex to process, models like the GFDL and HWRF for example, the model data is not done for hours. So the 18Z starting position of the late cycle models, which don't get released until 0Z, will have a different start position as the early cycle models which are initialized and released at 0Z. (or within an hour of that) The late cycle models usually have a starting position that is usually that of the previous early cycle models. (But some models, like the global models, have starting positions that are completely different, depending on where the global model initialized the storm.)
Take a look at the times under the Skeetobite model names and notice that some times are different. That explains the different starting positions, for the most part. I notice one of the Skeetobite start positions on the animation you posted was very off, so sometimes it does make a mistake. The crosshairs were at the start of the UKMET model rather than early cycle models for some reason.
Now some models, not that I see on the Skeetobite plot you posted, do have a different start position. The global models can be all over the place on their start positions, but the Skeetobite image you posted does not have those.
Here is an excerpt from the NHC model page about early / late models:
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"b. Early versus Late Models
Forecast models are characterized as either early or late, depending on whether they are available to the forecaster during the forecast cycle. For example, consider the 1200 UTC forecast cycle, which begins with the 1200 UTC synoptic time and ends with the release of an official forecast at 1500 UTC. The 1200 UTC run of the NWS/Global Forecast System (GFS) model is not complete and available to the forecaster until about 1600 UTC, an hour after the forecast is released. Thus, the 1200 UTC GFS would be considered a "late" model since it could not be used to prepare the 1200 UTC official forecast. Conversely, the BAM models are generally available within a few minutes of the time they are initialized. Therefore, they are termed "early" models. Model timeliness is listed in Table 1.
Due to their complexity, dynamical models are generally, if not always, late models. Fortunately, a technique exists to take the latest available run of a late model and adjust its forecast so that it applies to the current synoptic time and initial conditions. In the example above, forecast data for hours 6-126 from the previous (0600 UTC) run of the GFS would be smoothed and then adjusted, or shifted, so that the 6-h forecast (valid at 1200 UTC) would match the observed 1200 UTC position and intensity of the TC. The adjustment process creates an "early" version of the GFS model that becomes part of the most current available guidance for the 1200 UTC forecast cycle. The adjusted versions of the late models are known, largely for historical reasons, as "interpolated" models."
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See this page at the NHC for more on models:
http://www.nhc.noaa.gov/modelsummary.shtml
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