Just to state it explicitly: a "before update" trigger fires every time an UPDATE command is issued on the table the trigger is define for, without checking for modified columns.
An "after update" trigger will only be fired if SQLA has really updated some values. As a consequence your "dummy update" (2.) won't call an "after update" trigger.
Cf. the docs http://dcx.sybase.com/index.html#1201/en/dbreference/create-trigger-statement.html