tuuN, strictly speaking is for the second person singular and tusiiN is for the second person plural. However, in terms of respect afforded to the person spoken to, one would use the former for a person of same/similar age or younger and the latter for an older person.
You are likely to refer to a close friend of yours as "tuuN" but for your mother and father as "tusiiN" whether speaking to them individually or together.
I agree with what you say. However I have been told that this is a recent development. In the past there would have been a clear split between tuuN-singular, and tusiiN-plural, regardless of the formality or respect you were affording the person you are speaking to.
I was just trying to ascertain whether that was the case, and if anyone had an idea when tusiiN started to be used for 'respect'/formal situations. Perhaps it is clearer to ask: when did tusiiN start to be used for the singular (formal)?