Sophie,
It is possible for the bags to be damp while the growing mix is still relatively dry. If the moisture level of the mix falls below a certain level, it will become hydrophobic and push water to the sides... The bag becomes wet, but the growing mix is not saturated. I normally water my containers several times. I will water all of the containers briefly, wait a few minutes, then repeat with a more thorough watering. If I feel the containers are still not wet enough, I'll repeat a second time.
I do find the bags are a good indicator of when to water. I feel the underside of the bag. if it is wet, hold off on watering. If it is completely dry, I either water then or the next day depending on the weight of the bag. Your watering needs may differ slightly, but this is the gist of it.
Good luck.