The best thing you can do is a little training that also enriches the time you spend with your tiels. They do tend to be perch potatoes even when they are out of the cage and often just end up perching and pooping on you. That is how they spend time with their mate in the wild, perched side by side, resting: until they fly off with the flock for the next foraging trip.
Once your tiel is step up trained for your hand, introduce them to stepping off of your hand onto any surface. It is initially easier to teach them to step higher off your hand, and once they do this easily, then teach them to step down lower than your hand. That way you will never have a problem getting your bird off of you in an emerency situation. The other thing you should teach for safety and so you can hanndle your bird when they are upset or angry or hormonal, is stepping onto a hand held perch. My birds will step up onto any size or length of perch/dowel I hold out to them no matter where they are (six feet above my head or on the floor by my feet or under a piece of furniture). This is also safety training and very useful behavior to habituate into your bird. These training sessions are just ten to fifteen minutes once or twice a day, but really enrich the time you and your bird spend together.
Later you can teach little tricks, like turn around or open your wings or shake hands. It keeps your bird bonded to you and mentally interested. I run each bird through step ups every day so they don't forget to do it on cue, just one or two when giving a treat or offering a scritch as reward. If you can safely do it, you can also play real estate agent and take your bird to unfamiliar rooms to explore the house. This is also a safety idea so if the bird flies away from their usual area in a panic, they can find their way back to their cage after they settle down.
There is so much you can do with your bird if you just think about it!