Altium Interactive Routing - Auto-completing
What you're referring to is called "Look-Ahead" by Altium. It allows you to "preview" where the next trace will go without placing it immediately on mouse click. It sounds like you have it turned off. While routing, simply press the '1' key on your keyboard. The last segment of the track attached to your cursor should change from a hatched fill to no fill, which means the look-ahead feature is enabled. To disable look-ahead, simply press the '1' key again.

A couple images for reference:

Look-ahead enabled (places only horizontal hatched section on mouse click)-


Look-ahead disabled (places both hatched sections on mouse click)-