DSXchange

Sounds like it to me but that also seems that it would be a question best answered by IBM.

It is so weird, man.
We think that it might be the Java version.
But when I set JAVA_HOME variable at the job, sometimes it works at the first running. However, the other result executions are wrong.

When I copy the job and execute it for the first time, it works.
(the following executions record the date incorrectly again).
I got really confused, actually.

Any tip?

Only the same tip as before, I'm afraid - open a case with your official support provider. Let us know what they have to say about it.