Those controls are related to the Ingroup, not the Call Menu. The call menu allows people to navigate, but once they land where they belong ... the Ingroup controls what happens.
Read the Vicidial Managers Manual about Ingroups. The "Call me back" method is a bit complex and comes in several flavors, but is still part of the Ingroup (and I'm not sure if that part is in the Free or Paid versions of the manual).
I will note that it is possible to assign a Call Menu to an Ingroup (so that while the prospect is "in" the ingroup, any buttons they press are interpreted by a Call Menu ...), thus allowing the call to be pushed to another location which could (in theory) create a new lead in a new list in an OUTBOUND campaign which will be automatically dialed when an agent is available. It could also utilize a no agent call URL for the ingroup that moves the lead to that campaign instead. All sorts of methods available. All fairly intricate, though.
Never actually set it up for a client. Usually this means it's in the Manual (IE: Why would a client ask me to set up something that's in the manual? LOL)