I assume that you are asking about Charles Tiebout’s classic article from 1956 that is entitled “A Pure Theory of Local Expenditures.” You have asked other questions about that article and the content of this question makes sense in that context. I will answer on the basis of this assumption.
In the article. Tiebout sets up a model in which “consumer-voters” are able to express their preference for various levels of public services and taxation. They do so by moving from locality to locality based on the services and taxes in the various places. This model is based in part on the assumption that people do actually move from place to place because of the different levels of public services that are available.
In the real world, it is very hard to know if this does happen. One problem is that it is not always possible to know why other people move. Typically, people have a variety of reasons for moving. Some of them will have nothing to do with the level of public services. People will move to be closer to jobs. They will move to be closer to family. They will move because they want to have a bigger house. None of these have to do with Tiebout’s theory.
However, it does seem clear that levels of public services can play a role in people’s decisions to move. This often happens when people become wealthier and/or when they have children. I have known many people who have moved from cities (Seattle, for example), to suburbs (Bellevue, for example) because they had young children and felt the suburban schools were superior to the ones in the city. When people get richer, they might move to richer towns, in part to get things like better police service. These are some examples of people in the real world moving, at least in part, to choose different levels of services.