Yes, they can be territorial of their cage because their cage is their safe place. Some 'tiels don't warm up to hands unless there is a reward involved, but some do regardless. Just a hand moving can cause a negative reaction if your bird is particularly afraid. It all depends on their temperament to begin with and also how they've been treated by people in the past (for example if your 'tiel is a rescue).
Food bribery is a method I've had much more success with in my own flock in getting timid birds used to fingers and hands. They learn to associate your hands with a treat and therefore a positive experience, and eventually forget about your hand to get the food, and suddenly fingers and hands aren't such a threat anymore. You need to work at it several times a day, every day to have success.