Depends on which a/c we talking about..
First answer,a/c forsure will change your cruise alt. automatically.
About second one,if aircraft on alt mode Airbus would just remind you about making a step climb as pop up a text msg to cdu.The altitude you set to the fcu is the essential input source to manage the a/c.As far as i know about boeing is beginning to descend if you pass over t/d point and set to fcu a lower alt;i dont have any idea about climb process..
If you mentioned cruise alt which is shown at fmgs,yes both cases it will change automatically.
Hope it works
