In Twins (1988), first Professor Mitchell Traven denies knowing anything about them, then changes his mind after they break through the door.
Why didn't he have them taken away by the security guards who came in?
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Because they frightened him.
You can call guards in to take them away and they might actually manage it(!) but what happens when you leave work? You will not always have guards to protect you, who knows how far these two will go? Who wants to find out too late that they are lunatics with a basement, a gag and a blowtorch?
It is much easier to just give them what they want and let them be on their way.
Traven decided he wanted to talk to them because he was shown proof of who they were (the picture). And because it appealed to his egotistical personality. Yes, he was afraid of Julius, but that is not his only motivation.
His original action was a knee-jerk reaction. He ordered them off because the project was still a secret. Then Julius became persistent and knocked down the door. But this gave Traven enough time to think. His next action was the result of several things at the same time:
Please note in the clip below (at about 1:07:21) how, when Julius confronts him with the picture, Traven looks at the picture, then at Julius, and then at the picture again. (I could not find one that is better quality.) It is at this moment that Traven realizes that Julius is the real thing.