I have a DeckLink Pro card (SD) and have a green tint. The tint is visible primarily on black and white files and primarily through the component out of the card rather than through the composite out. You might want to review the thread initiated by davemcc on 3 April on this forum and the thread initiated by Kai on 23 March on the Decklink forum for more information. I alerted Blackmagic to this problem three times since June of last year. Their support has not been able to duplicate the problem and I have just received authorization to return my card for repair and/or replacement. You want to compare the view in the monitor through both the composite out and the component out of the card and you want to check for any ground loop problems. If no loop problems and if the composite out is clean but the component out has the green tint then you may want to contact Blackmagic about repairing or replacing he card. Good luck. By the way, I have a JVC BM-H1310SU monitor which I believe is similar to the Panasonic monitor you have.
michael d