The following rules govern the visibility of data changes in functions that use SPI (or any other C function):
During the execution of an SQL command, any data changes made by the command are invisible to the command itself. For example, in:
INSERT INTO a SELECT * FROM a;
the inserted rows are invisible to the SELECT part.
Changes made by a command C are visible to all commands that are started after C, no matter whether they are started inside C (during the execution of C) or after C is done.
Commands executed via SPI inside a function called by an SQL command (either an ordinary function or a trigger) follow one or the other of the above rules depending on the read/write flag passed to SPI. Commands executed in read-only mode follow the first rule: they cannot see changes of the calling command. Commands executed in read-write mode follow the second rule: they can see all changes made so far.
All standard procedural languages set the SPI read-write mode depending on the volatility attribute of the function. Commands of STABLE and IMMUTABLE functions are done in read-only mode, while commands of VOLATILE functions are done in read-write mode. While authors of C functions are able to violate this convention, it's unlikely to be a good idea to do so.
The next section contains an example that illustrates the application of these rules.