Yes they are, and they're pretty self explanitory. Talk to a digi, get the quest, wander around the base and find the digi of the same type as the one you got your quest from (dragon, bird, etc). You'll hear a chime, and then when you go to the warp square, one of the regions will be flashing "quest".
That's where you'll want to be going. Some quests require you to find something (in a chest), or defeat monsters, or as you progress, both. Each time you complete part of the quest, you'll hear the chime sound.
Once you're done, talk to the digi in your base again. The chime sound should happen again. You can then go back to the office and collect your reward.