The AutoComplete control must be aware of the data to enable this feature. I am enclosing a sample which demonstrates what you are looking for.
It consists of a form with a combobox and an autocomplete control. Here is how the AutoCompleteControl gets it''s data:
this.autoComplete1.DataSource = this.itemsList;
The combobox''s AutoComplete on autocomplete property is set to both.
There are more samples in the \Syncfusion\Essential Suite\Tools\samples\Editors Package\AutoComplete directory.