Hi! Sorry for the delay in our reply. Both @LynneBuie and I were swamped with the Esri User Conference this week. But I'm so glad you brought this to our attention. The documentation is not clear at all, as you mention. The table, here, does indeed correctly document the fields that are added to the Input Space Time Cube (STC) after you run Emerging Hot Spot Analysis (EHSA), but it doesn't document how to interpret the fields that appear in the EHSA output layer results (as you found). Hopefully, this will help:
The EHSA tool runs Gi*, comparing each bin and its space-time neighbors to the Global Window (Entire Cube, Neighborhood Time Step, or Individual Time Step) to determine if the local values are significantly larger (hot spot) or significantly lower (cold spot).
Once all bins in the cube have been assessed (for the categories shown in the graphic above), it runs Mann-Kendal on the Gi* Z-Score values to get the trend for each location (column).
The PATTERN field in the EHSA output layer is one of potentially 17 different categories documented here. If you read the description for each category, you'll notice that to classify each location, the tool needs to know the count and percentage of significant bins and if they are hot or cold... and if they are at the top of the cube (most recent time steps) or not... And for most of the patterns this is enough, but to determine if the hot bins are intensifying or the cold bins are diminishing it computes Mann-Kendall on the Gi* z-score values. The TREND_Z, TREND_P, and TREND_BIN values in the EHSA output layer are those Mann-Kendall results.
If that doesn't answer your first question, please ask again and I'll do my best to clarify.
For your second question, you want to visualize the EMERGING_{ANALYSIS_VARIABLE}_HS_BIN. The 3rd column of the variable table indicates that particular variable is available in 3D. To visualize it, there are two steps:
1) Insert a NEW SCENE (select New Global Scene if it makes sense to show the curvature of the earth, otherwise select New Local Scene).
2) Run the Visualize Space Time Cube in 3D tool.
Then you can navigate around the 3D scene with your mouse.
I'm not sure if this will be helpful to you or not (it's NOT based on raster input), but @KevinButler-Analysis and I created a Learning Path for a workshop we did for UCGIS.
I hope this answers your questions. If not, please let me know and I'm happy to try again.
Best wishes,
Lauren Griffin, Esri