That's pretty much how Germans use their 2nd person singular and plural ("Du" und "Sie", respectively) - usually, only familiar people, or children are addressed with the singular. Amongst adults the 2nd person plural is standard, and formally correct is to "offer somebody the 'Du'" as a token of familiarity and friendship, though that is changing, too. In the olden times, children would address their parents with "Sie", whereas the parents used the "Du", as a sign of the difference in rank. Using the singular with a stranger (especially when they've used the plural form before) can express contempt - a sign that you don't take them seriously.
The 2nd person plural is more formal and distant, and can hence be used as an exhortation to behave like an adult - bit like what your granddad did with you. My teachers switched to the 2nd person plural once we completed the secondary education first stage (German equivalent of high school) -most would offer us the "du" again, but one flat-out refused to address us with "du" again, stating that now that we had completed the mandatory part of schooling, he'd address us like adults and expected us to behave accordingly. Definitely grabs your attention.
As a TA, I use the 2nd person plural when I address students - some try to get me to use the singular, and I don't get mad at them when they do, but I stay with the more formal plural.