One-to-one is used when you talk about transfer or communications. You may use one-to-one when you can identify a source and a destination. For eg., a one-to-one email is one sent from a single person to another, i.e., no ccs or bccs.

Understanding the Context

In maths, a one-to-one mapping maps one element of a set to a unique element in a target set. One-on-one is the correct adjective in your example. See Free ...