It's true that all compute processing takes place on the server. However, if you reference local data sources (SAS data sets, Excel files, etc), these must be read and moved to the server for processing, and that can consume resources on your PC.
I'd suggest working with SAS Technical Support to diagnose the situation. They will probably ask for a sample project and log that shows the symptoms you're seeing, and might be able to advise how to optimize it.
Chris