You are experiencing very common and perfectly normal behaviours.
Your birds want to be around you , so you have definitely done the right thing.
Taking time as you yourself said, is the way to go patience and trust are the winning formula.
When you sit near the cage talking to them ,gently place your hand next to the cage to start with. work up to having your hand inside the cage with them not being bothered by his. It will take time but keep on being interactive and spend as much time as possible so they do learn to trust you.