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. 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 ...
Some people say a dog=one, dogs=ones, the dog=the one=that, and the dogs=the ones=those. It's a rule of thumb, but what I found was that this is not always correct.
How one and one's is different from other indefinite pronouns The possessive of one (one's) is formed the same way as the possessive of other indefinite pronouns, such as someone (someone's), but it is used a bit differently. For most people, one is consistently used with the possessive form one's.