I think that's how it's always worked. You finished up yesterday's quests and it let you pick up today's. They did change the reset time a little while back, so maybe that's why it feels new to you.

You can hold onto a daily and turn it in the next day, then receive a new one, with one important caveat: you can't do the exact same permutation of a quest twice in one day.

For example, if you received "Madness in Grahtwood," then held onto it for several days, then turned it in, you might not receive a new daily quest from Alvur Baren because he would've given you "Madness in Grahtwood."

Another good example is pledges. You can't, say, hold onto the Scrivener's Hall pledge until Urgarlag is offering that pledge, turn it in, and pick it up again.