Here is a link to how the Hot Spot analysis works in ArcGIS: Link
This portion of the explanation probably contains the clue to why that area flagged as a hot spot even though most of the values were zero.
To be a statistically significant hot spot, a feature will have a high
value and be surrounded by other features with high values as well.
The local sum for a feature and its neighbors is compared
proportionally to the sum of all features; when the local sum is very
different from the expected local sum, and that difference is too
large to be the result of random chance, a statistically significant
z-score results.
When you say that 10 of the 13 "Hotspot" points had zero values, I am assuming you refer to your input emissions points that fall within one of the areas identified as a Hotspot. Even though many of the points in that area are low, the small cluster of high emissions value points which makes up the "local sum", may be different enough from the "expected local sum" as to be statistically significant.
As you have noted, the area of analysis is determined by your distance entry. The question that arises is whether you used the appropriate distance in your Analysis. You stated a couple of different things in your question. The first was that you used the "Default" distance as determined by the Spatial Autocorrelation tool. The second was that you used the "Derived" distance. It is unclear what you mean by this, though I think you are referring to the default distance derived by Spatial Autocorrelation tool.
It is important to realize how this "Default" distance is calculated, and what it means.
FIXED_DISTANCE_BAND
The default value for the Distance Band or Threshold Distance
parameter ensures that each feature has at least one neighbor, and
this is important. But often, this default will not be the most
appropriate distance to use for your analysis.
It looks like this default value is calculated the same way as that for the actual Hot Spot analysis tool if you were to use it's default setting.
This help section discusses Selecting a fixed-distance band value. Essentially, using the default distance value ensures that each point has at least 1 neighbor. This may not be enough to determine whether there is spatial autocorrelation in your points. You can use the Spatial Autocorrelation tool to determine the optimal distance for your Hot Spot Analysis. It is an iterative process in which you evaluate different distances to see which one gives you the Peak "z-score". The z-score is an indicator of statistical significance. It doesn't say whether your data are clustered or dispersed. It simply says that there is significant spatial component to the values in your points when evaluated at a particular distance.
The key then is to determine the optimal distance that you want to use in your Hot Spot Analysis. Once you run the tool, then evaluating the results will be the combination of the z-score and p-value. Having a high z-score will indicate that the values in that area are higher than the expected values would be. A low p-value indicates that there is a low probability of the hot spot in that area being the result of a random process.
To jump back to your results for a moment, it is possible that while the area in question has a high z-score, indicating emissions that are higher than the norm, if you were to symbolize based on p-value, you might see that they are have a high value, indicating a higher probability of being random, and thus not significant.
Something else to think about is that using different distances may be relevant in the context of the scale you are interested in. A small distance may reveal hotspots locally, where a larger distance may show hotspots in a regional context. As well, it may be useful to evaluate your results in conjunction with results of the Spatial Autocorrelation analysis. This link has more detail about that analysis, as well as a FAQ at the end with some interesting discussion.
Hope this helps!
