EITHER or BOTH, main applicant and secondary applicant, can need to prove their English proficiency. It's needed for the secondary applicant if his/her qualification is needed for extra points for the EOI. And it always comes down to IELTS to resolve any doubt in the CO's mind. (Examples of why a CO may doubt evidence. A few years ago, there was a big upheaval in India when a lot of institutions were found to have been selling fake proof-of-English letters. This had a knock-on effect afterwards for many applicants who had genuine letters from Indian universities, but INZ didn't trust them, and asked for IELTS anyway. Also, longer ago than that, there was a poster on the forum who got asked for IELTS after his CO interview. He had a university letter, and that had been accepted, but during the interview, he couldn't understand a lot of the questions, or make the CO understand what he was trying to say, which made the CO doubt that the letter could be genuine. I wasn't surprised with this news, having seen the English in his posts. He didn't get the required level, or the visa.)