Luna wanted to gain Alex's trust.
She knew that she had to do it if she wanted a place in his heart, but she also knew that it was going to be anything but easy.
Trust is built slowly, step by step, it can't be done in a single step unless you save someone from a certain death situation by sacrificing something that is very important to you.
However, Luna knew that the latter option was not plausible in Alex's case since he was way stronger than her, so she decided to go for the former one – build trust slowly.
The action of signing the contract given by Alex even without reading it showed that she trusted Alex enough not to care about what Alex was doing.
But then she went ahead and ordered her subordinates to do the same.
This was a way to gain a bit of Alex's trust and looking at him lightly nodding his head with his brows raised a bit, she knew that she did manage to get his interest even if she didn't get his trust.
