No, since the students have apparently already started the assignment you would say "the students have been doing the assignment since the day before yesterday."

Your answer is a great help. We have such written forms on exam. Is this sentence correct?.... 'The students will have been doing this assignment since the day before yesterday' I am confused about time phrase.

I'm a native speaker and I'm embarrassed to admit I had to look up which tense is the "future perfect continuous." 

When we say "You will have been studying English for two years when you finally understand this tense," we mean:

- you have not yet begun to study English, but you are definitely going to do so at some point in the future.

- once you do begin, after two years you will understand.

This is a very rare construction and you are unlikely to hear it used verbally, although you may see it written. I would be much more likely to say:

"You'll have to study English for two years before you understand this tense."