Are triggers and their results visible in same order as original operations?
Yes, that is guaranteed, because there is no chance that the trigger function for two updates of the same row will be executed at concurrently.

The UPDATE will get an exclusive lock on the row, and the trigger function will run after the update. The transaction (that holds the exclusive lock) will not complete until the trigger has run, so no concurrent UPDATE can get the lock and start running until the previous one is done.

An exception would be if you had defined the sequence with the CACHE clause, so that backends can cache sequence values, but you didn't do that.