Hi,
Firstly for a dual employment you should be clear that as per the company norms stipulates about dual employment. In case it is not them it is a violation.You may have chosen dual employment for economic reasons or whatever, the undertaking should have been legal.
However happend is happend weather is was done intentionally or unintentionally, you have to set right the anomaly. You can request your old HR Colleagues to provide a good reference about you, to an extent it will mitigate your problems.
All the best for your new assignment.
Regards.