My tutor definitely spoke Spanish to me, but the first several months was all in English. I hate the teaching method where a teacher just yammers away in the target language, as if (again) by magic and special miming gestures, the students will 'pick it up.' Bleh. Nieves gave me a review of concepts in English first, then we practiced speaking. I can't imagine learning any other way - but that's probably why she taught me that way. That's the benefit of a private tutor.
This is usually the difference between a trained teacher and someone who's teaching to earn a bit of money. When English speakers go and teach English abroad, it's normally to give already-fluent people conversation practice. They don't have the training to be able to teach beginners effectively.
It is remarkably difficult to drop your language to a beginner's level. You need to remember exactly which tenses the students know (which may just be the simple present) and their extremely limited vocabulary.
The best lessons I had were where the difficult concepts were explained in English, but the majority of the lesson was in Spanish. I think a lot of teachers view dropping to English as cheating or breaking immersion, so they don't do it.
> Immersion is overrated
> Everyone else will just cringe after a few minutes and change to English
It's not really immersion if you aren't forced to speak the language, and form and maintain social relationships solely in the target language. It sounds like you weren't able to achieve that on your own in your day to day.
> Hire a private tutor
This is good advice. Your tutor was presumably speaking Spanish with you, which was the missing piece.
The takeaway should be if you're not part of a social group that speaks primarily (if not entirely) in the target language, then you will not learn it well.
Languages are a way of bonding between people. A single person raised alone in the wild has no language; a group of people in the wild always do.