"Once I have a t-SNE map, how can I embed incoming test points in that map?
t-SNE learns a non-parametric mapping, which means that it does not learn an explicit function that maps data from the input space to the map. Therefore, it is not possible to embed test points in an existing map (although you could re-run t-SNE on the full dataset). A potential approach to deal with this would be to train a multivariate regressor to predict the map location from the input data. Alternatively, you could also make such a regressor minimize the t-SNE loss directly, which is what I did in this paper.
Implementation can be found in the
Rtsne
package https://github.com/jkrijthe/Rtsne. But there is no transform/predict method available, see the discussion here https://github.com/jkrijthe/Rtsne/issues/6 and from the FAQ: