Yes, there was a time I did work at the zoo (I study animal behaviour and worked there for a short time). I was lucky enough to be there at a time when this little guy was young and small. Now he is a grown up huge male tiger and not so friendly to humans any more
Well, if you handle them every day, they remain tamed - like in those Thailand Buddhist temples, where they are like home pets. However in most of zoos they try to make animals remain 'wild' in a way. So as soon as they get too big to play with, people stop handling them. And never get in the cage together with tiger in it after that. Due to safety reasons mainly.