Ethics - Asking someone to work for free
In academia, it is not common to ask people to work for free. It is also not common to ask people to work, full stop.  What is quite common, though, is to see people seeking work in academia. This include people looking for funding to help them developing their research ideas, and people looking for opportunities to join someone else's research projects.

You came to the professor seeking an opportunity to work with him. The professor did not offer to fund you, but instead offered you an opportunity to work without compensation for a period of time. You can take this opportunity or leave it. If you take it, the funding may or may not come in 3-4 months. You are free to quit this arrangement at any time, before or after the initially agreed period.

The professor did not want you to do his work. You wanted to do some work with him and he offered it. You also wanted some money and he did not offer it. You make the story look like you were deceived or forced into unfair relations - no you were not.

There is no insult in offering someone to work without payment. In some countries such an offer is illegal, and in some universities it is not permitted to work voluntary. This is done in order to comply with employment laws in a particular country. However, you seem to imply that this is somehow unethical or not normal in a weird way - no it is not. 

BSc and MSc students often work on their own projects which contribute, sometimes significantly, to projects run by employed academics. Obviously, BSc and MSc students are not compensated financially (on the contrary, they sometimes have to pay tuition fee), but they use the feedback they receive in order to learn new skills. PhD students in some countries get a stipend, while in others they have to pay tuition out of pocket. 

You have just completed your master, and have not yet got a PhD. From what I see, the opportunity to work on a project, receive a feedback and learn from it, with a chance of future employment, is not an unfair offer. Whether it is good enough for you to take it, you have to decide yourself.