Ontology Design is the Development of Ontologies. Ontology Development is an iterative Process, which means step by step one refines and extends the Ontology. Of course, sometimes one has to go back. So it is an iterative Process that repeats continuously and one improves the Ontology by doing this.
There is not an only single way to develop an Ontology. In fact there are different ways for modeling an Ontology. In practice it is always the designated Application that decides about which modeling Approach to choose, i.e. which cycle to repeat and how to go back in this development Process.
There must also be place for the Formulation of complex Axioms including Property Constrains but one also needs to make Rules or other type of Constrains concerning the Classes that they should obey, then one should consider to include the Definition of Axioms that are needed for the Knowledge Base and the Ontology and Knowledge one wants to represent.
On the other hand the whole process has to fit for large scale industrial Ontology Engineering, including Version Control strict Evaluation and Quality Assurance in a professional Engineering Process.
There is not one correct way to model a Domain and there are always viable alternatives.
in practice the designated Application decides about the modeling Approach
Formulation of Axioms
"There is no one correct way to model a Domain. There are always viable Alternatives."