Not physically I don't believe. Just threatening her not to cross him because people in her role have come and gone over the 30 years but this is his world. He has control in the park and also even with the current Board compared to her. This was the table that she sat at as a child and he is sitting exactly where her father sat during that meal. He knows about her relationship with Bernard and will use that if he has too also.
From the showrunners on the conversation between Dr. Ford and Cullen:
"...we were also excited about this moment where you were reminded about the sheer power that Ford can command as the creator of this place. You can imagine Walt Disney having a lunch at Ariel’s Grotto in the middle of Disneyland and commanding all the roller coasters to stop all at once. There’s an extraordinary power there."
"In the pilot, Ford felt a bit like the Lion in Winter, that he might be stepping back. Here, we’re reminded that you underestimate this guy at your peril. He has his own designs of what he wants this place to be. You’re also reminded he has an extremely controlling relationship with the hosts. Like the moment when he cuts a host’s face open and you realize why they’re all stripped bare in cold storage, that it’s a very practical measure on his part to make sure nobody makes Arnold’s mistake again, that treating these hosts as machines is vital to ensure that the techs who work with them don’t mistake them for people. You’re reminded that Ford is not a friend to the hosts. He’s a father figure and that can go a number of different ways."
