Rex threw his hoodie over the face cap he was putting on so as not to be recognised by passersby. No matter how happy he was to see her, risking the chance of people recognising him wasn't something he was ready to do. He quickened his pace, making sure not to lose track of the person he was following while at the same time making sure he wasn't being followed.
With each step he took towards her, he could hear his heart beating so fast to the point he thought it was going to bounce out of his chest in the middle of the road.
If it were to be in another situation, he would have just approached her, but when you have a bunch of policemen after you, you should know better than let your guard down.