Third to First- Is it a balk if he doesn't disengage.

[Gre144]

Fed Rules- Runners are on first and third.

Coach came up to me and said the pitcher balked in his third to first move because he didn't disengage from the rubber as he threw to first. ( brought up this question in a previous thread but I kept on getting conflicting answers)

I told the coach that it is not necessary to disengage the rubber but the pitcher must step towards thrid and fake there before he goes to first. (I used this explanation from several responses to my previous thread on this topic).

Also, I wasn't sure how to explain to him the definition of stepping towards a base.

In short my question in two-fold-

1) Does the pitcher have to disengage from the rubber in his third to first move at the moment he throws to first?

2) What is considered a step towards a base?

Thanks,

Greg