SSIS: Making an Informix transaction local doesn't work

For a single SSIS task I'm trying to make its transaction local. To simplify things, I'm trying to do it like this:

• create the new package
• create just one Execute SQL Task

• inside that task I delete some rows from destination table and issue a ROLLBACK:

  DELETE FROM SOME_TABLE WHERE SOME_COLUMN = 'ABCD';

  ROLLBACK;

• I create a new Connection Manager for that task (IBM Informix OLE DB Provider) and make sure it passes Test Connection
• after adding the task, I change its TransactionOption property to Required
• after that, I change the RetainSameConnection property of Connection Manager to True

As I understand, the task should start a local transaction without using DTC. However, this is the output when I run the package:

SSIS package "Package1.dtsx" starting.

Information: 0x4001100A at ROLLBACK: Starting distributed transaction for this container.

Error: 0xC001402C at Package1, Connection manager "xxx@yyy": The SSIS Runtime has failed to enlist the OLE DB connection in a distributed transaction with error 0x8004D01B "The Transaction Manager is not available.".

Error: 0xC0202009 at Package1, Connection manager "xxx@yyy": SSIS Error Code DTS_E_OLEDBERROR. An OLE DB error has occurred. Error code: 0x8004D01B.

Error: 0xC00291EC at ROLLBACK, Execute SQL Task: Failed to acquire connection "xxx@yyy". Connection may not be configured correctly or you may not have the right permissions on this connection.

Task failed: ROLLBACK

Information: 0x4001100C at ROLLBACK: Aborting the current distributed transaction.

Warning: 0x80019002 at Package1: SSIS Warning Code DTS_W_MAXIMUMERRORCOUNTREACHED. The Execution method succeeded, but the number of errors raised (1) reached the maximum allowed (1); resulting in failure. This occurs when the number of errors reaches the number specified in MaximumErrorCount. Change the MaximumErrorCount or fix the errors. SSIS package "Package1.dtsx" finished: Failure.

Does anyone know what's happening here?