Row locking within a SELECT statement

The following documentation comment has been logged on the website:

Page: https://www.postgresql.org/docs/9.4/static/explicit-locking.html
Description:

After experiencing frequent deadlocks, I'd like, please, the docs to clarify
the question/situation:

Are FOR UPDATE locks "atomic" within the SELECT that acquires them, or do
they lock rows "on the go", as they are met in the query results?

Scenario: assume I have an `alerts` table which receives rows from random
sources,  and then they are processed by severall passes of stored pl/pgsql
procedures.

In order to avoid concurrent manipulation of rows, I do issue a "SELECT ..
FOR UPDATE" on the sets of rows, before UPDATEing them (because UPDATEs
cannot be ordered).

transaction A {
SELECT .. FROM alerts WHERE <clauseA> FOR UPDATE;
... decide ...
UPDATE alerts ...
}

transaction B {
SELECT .. FROM alerts WHERE <clauseB> FOR UPDATE;
... decide, sort, filter ...
UPDATE / DELETE alerts
}

Still, those 2 transactions *do*  deadlock.

Otherwise, should advisory locks be used instead?