The volume is controlled by your device, and that's why it is instant.
The media you are playing is being transported over WiFi, and is therefore subject to a number of speed-influencing issues including:
Internal/External Causes (Streaming from a home device such as a computer on the same network, some issues also cause problems to external sites and services like Netflix)
- Distance from Airport
- Different vertical levels from Airport (eg. First to Third Floor). Wifi prefers to travel horizontally.
- Interference on the channels caused by several devices using the same WiFi "channel"
- Speed capability of Airport and Media Server
- Hardware (sending and receiving devices experiencing hardware issues)
- Software (sending and/or receiving devices experiencing software issues)
External Causes (Internet)
- Internet outage or issues that are out of your control, and usually last 15 mins to several hours, but not a permanent problem.
- Router is having connection issues with ISP (hardware failure, communication errors, etc.). This would be a more regular problem and requires a tech support call to your ISP.
- Streaming service (eg. Netflix) is having issues (Generally, there will be some kind of website update if this is a widespread issue affecting all customers)
You should monitor whether you have this problem all of the time, or some of the time, and try to isolate the situations where it seems to be at it's worst. Keep in mind that streaming from the Internet is completely different than streaming from your internal Network.