Partly.
Some of the vision we saw of Jade and Drew in their room during the marriage task showed them flirting and behaving in similar ways to how they are now - so that really type of behaviour hasn't change all that much. However Tully has been constantly bringing up Jade with Drew for the last week and a half or so, definitely since the night of Jade's birthday, questioning how he feels about her and undermining Jade and emphasising how Drew will be seen by others - making him question how Jade acts and what her motivation is - while actively encouraging Jade towards Ed. She has told him that she is the only one that is concerned about him. In the unrealistic environment of the house, where strategies are always in play, it's been pretty easy for Tully to work on Drew, and for him to believe t the picture Tully is painting. He is now seeing Jade as suspect, and Tully as the person he can trust.
I think Tully has two motives - one is divide and conquer (Jade and Drew were very close), and the other is that she is attracted to Drew and jealous of whatever place Jade holds with Drew.