David Klee shows that you can put an AFTER trigger on a memory-optimized table in SQL Server 2016:
SQL Server 2016 supports AFTER triggers! I could find no good example of how to do this with a project I’m working on, so I figured out how to make this work. The following before and after screenshots are from a SQL Server 2016 instance and the DVDStore3 package. I modified a trigger to work with In-Memory OLTP.
Click through to see the code.