Trigger should get automatically executed once DML operation invoke/completed.
The buildfarm proves that a stock community 16.2 install has functioning triggers. Whatever is going on is specific to your situation and most likely not a bug. I'd suggest posting for help to -general with more details including the evidence for the simple test you performed below.
Further I have created simple new table and trigger on it, still it is not invoked after update statement.
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I have provided required grants "SELECT, INSERT, UPDATE, DELETE, TRUNCATE, REFERENCES, TRIGGER" of that table to user. Provided all usage schema to that user. Given ownership of trigger functions to that user. Still there is no trigger executed except insert / update / delete operation runs OK.
None of those actions are expected to make a difference. You would have seen permission errors if they were relevant.
