Have I offended my professor by applying to summer research at other universities?
Tell him that you do intend to participate as previously agreed, but that funding for the summer was an important consideration. If he is at all reasonable, then that should be enough. If he is offended, then he isn't being reasonable.
If he offers you summer funding, then consider that, of course, but he should have little controlling say over a volunteer.
Perhaps he values your work so much that he thinks losing you for the summer would be a blow. Alternatively, he is just a jerk. If he hasn't got a reasonable response, you should find a way to be done with him. What he did is unprofessional, probably unethical.