I have a feeling that this usage - which I personally find highly irritating, because it suggests either that the initiator of a conversation is helping a person who is in dire straits or that they themselves are in trouble and seeking help from a lifeguard figure - became popular in California, but is that correct?
Reach out and touch someone -- AT&T Commercial 1987
It's supposed to be warm and fuzzy. I don't know where AT&T got it, or if they made it up.
A little more searching suggests that it comes from a Diana Ross song; Wikipedia:
Reach Out and Touch (Somebody's Hand)" was the debut solo single of Motown singer Diana Ross, released in April 1970.
As for the psychological and social significance of the phrase, see the Psychology Today article When AT&T asked us to ‘Reach out and touch someone’, did they mean that literally?
The article points out that today, with cell phones ubiquitous, the phrase might mean the opposite of what it did in the 80s. Today, it might mean get off your phone and pay attention to the person you are eating dinner with.
See Meaning of "reach out to somebody" for many interesting answers on what "Reach out" means; the consensus is that it is twaddle. (Note, the older question does not ask about the origin of the phrase, thus the current question is not a duplicate.)
To "reach out" is simply a reversal of the word "outreach" to make it a verb.
According to Merriam Webster, the word means : the activity or process of bringing information or services to people and has been in use since the 1870's.
In modern usage, it can have a submissive context; as in extending an olive branch, or approaching someone with an offering of peace or goodwill. It's meant to be polite, not necessarily a suggestion of helplessness.