Can anyone help me to explain why early rise will invoke the heel turn? Thanks

Because your partner needs to feel the rise so she knows to bring her feet together in preparation to do the heel turn.

Right at the time of beat "2", the feet is ALREADY closing or START to close?

Early rise posted by dancelover2012. Are you looking at this question as a male. If you are, and this is Foxtrot, the instructions are very clear. They are rise at the end of the first step. Which means you are going onto your second step from a toe to a toe ( and not to commence to rise which would be wrong ). If you are coming off a flat foot you are totally wrong. Just follow the technique book. Don't forget to sway on steps 2 and 3 as well as CBM on step 1.

"Can anyone help me to explain why early rise will invoke the heel turn? Thanks"

Especially as there are heel turns which do not formally feature "rise" at all, it will probably be more practically useful to focus instead on the difference in use of the knee during the first step.

In a follower's heel turn, the knee (of both partners) remains "braced" which is to say relatively straight in comparison to in a conventional (waltz-like) turn where there is a notable bending of the knee to absorb arrival, and a re-straightening during departure. Simply using his own knee in one way or the other will be sufficient to allow the man to communicate his intent to a follower who is moving with him.