What does 按部就班 mean?
按部就班 is not wrong and is in fact etymologically more correct:

選義按部，考辭就班 （陸機《文賦》）
To obtain choice ideas in close observation of things in categories, and elect expressions that will fall in happy order (trans. Chen Shixiang 1951)

This was an advice by Lu Jin from the Jin dynasty on how essays should be written. Of course in modern Chinese the idiom has evolved to describe things other than writing.

Is 按步就班 wrong? Etymologically, definitely yes, but it is understandable, and there are cases where these variants that appease the modern reader become acceptable. Consider the etymologically correct 名副其實 （曹操《與王修書》） and its variant 名符其實. Personally, I would stick to 按部就班 and 名副其實. You should especially do so if you are taking a language exam. I would also interpret 部 and 班 in classical Chinese – good practice if you are learning idioms.

Also, try not to interpret 按 as 'to press'. It is similar to meaning 按照 ('according to') here.