This is a safety issue spicy...the ash fallout was, according to Met reports, heading to Bali airport and its Flight Information Region (FIR) responsibility. Therefore, the airport bosses closed the airport, until a certain time, when the predicted winds were determined to move the cloud elsewhere.
Once the airport was re-opened it is up to the airlines to take their own safety responsibilities and act accordingly. This may be determined by many other factors like the route flown, the destination and alternate airfields available etc. Also, it may be determined by how much fuel can be carried and how far a deviation from the fligh-plan route can therefore be accepted. Many factors will go into each airline's determination to operate or cancel or, if airborne, to divert. Cathay Pacific, I heard from a crew member, landed in Singapore.
The horror of flying thru' a volcanic ash cloud was first understood in the following link .....
https://en.wikipedia.org/wiki/British_Airways_Flight_9
I shudder when reading because in late 50's I regularly flew a military 4 engined aircraft (piston not jet) at 10,000 feet reasonably close to this volcano in Hawaii...... not thinking of the ash consequence....
http://i.ytimg.com/vi/pVqOfTNzWN4/hqdefault.jpg