Your organisation’s online presence should manage customer expectations regarding response times. Users don’t mind waiting for answers if a) you are clear and consistent as to when you’re available, b) you provide contact details in case of emergencies.
On Twitter and Facebook, clearly list your hours of availability in the description. It is also worth reiterating them in your daily greeting and sign off. SouthWest Trains (@SW_Trains) are a great example of both managing expectations and efficient response times.
Post an emergency contact email address or link for out of hours (should your company deal in anything that is time dependent). If it’s just a case as to someone asking some advice, then users can wait until the next working day. Ensure your users know that they can DM you if required, monitor your DM channels regularly.