In general, points (both EPs and SPs) can only be spent during a run that your character is not in.
More precisely, they can only be spent between runs, except not between two runs that you are in (not that they have to be spent during the specific hours that the other run is taking place). Point-spending is considered to take place during a "training montage".
If you are learning a shtick from an outside source, the training montage has to take place where the source is. Some amount of travel from where a run ends up will be permissible, but not a lot.
The one exception to this is your Inherent skills - you can spend points in these at any time.