Is it the usual practice in a Japanese class that when writing in kanji and kana your teacher tells you to use furigana over top of the kanji you're writing in order to demonstrate to the teacher that you know how to say the kanji out loud correctly? I guess it makes sense but I was slightly taken aback.

I wouldn't say it's usual practice, but everyone is different.

It depends on the situation. It's a reasonable thing to ask for, I think, in a lower level class. I have specifically asked students not to use kanji or to write furigana in times like that -- particularly for the native Chinese students, I want to make sure they know the Japanese word and aren't just writing the Chinese characters they already know. But even for the non-Chinese students, kanji can let you get away with a lot. I know that many of the lower level students I have taught couldn't tell you whether 小さい is ちさい or ちいさい, how to correctly write 高校 in hiragana (こうこ？こうこう？ここ？）, whether 三つ is みつ or みっつ, whether 帰る is かいる or かえる, and such.