pg_stat_all_tables not updated when VACUUM ANALYZE execution finishes

Hi,

I face a surprising behaviour with VACUUM ANALYZE.

For a table with a structure like like this (and few records):
create table my_table (
my_column numeric
);

When I run the following:
VACUUM ANALYZE my_table;
SELECT relname, last_analyze, last_vacuum FROM pg_stat_all_tables where
relname='my_table';

The select returns null values for last_analyze and last_vacuum.

However if I wait a little between the end of VACUUM command and the
execution of the select the last_xxx columns have non null values.

So it looks like something is done asynchronously here but I'm not sure
what?
* Is it the vacuum itself that run asyncrhonously or the update of or the
content of the pg_stat_all_tables view?
* If I execute another query right after "VACUUM ANALYZE" is it expected
that this other query will benefit from the analyze done in the VACUUM
ANALYZE call?
* Is this a bug or a normal behaviour? (I'm using postgresql 9.6)
* Is there a way to wait for pg_stat_all_tables to be up to date? To give a
bit of context I was planning to use this information in the assertion part
of a test case I wrote to check vacuum were executed as expected but my
test is flaky because of this behaviour.

-Seb