This is on a model-driven app form, for the lookup field?
In this case, the control won't natively do full-text search. It will, however, use the entities' Quick Search functionality (searching against other columns), to help search against other columns.
You can train user's to use wildcards (*) like *Customer to perform this kind of search. It's not obvious, but if they are able to learnt his behavior, then it can be used in other places as well for leading/trailing wildcard searches.