As of February 2017, this problem still exists.
With VNC Viewer iOS (or for any platform), when macOS built-in firewall is turned on, the VNC client just hang (waiting to connect) and finally timed out. As soon as I turned OFF macOS built-in firewall, VNC client can connect.
My setup:
1). System Preferences --> Sharing
Remote Management: checked
Computer Setting --? VNC viewers may control screen with password: password entered
Message show: Other users can manage your computer using the address [my ip address here]
2). System Preferences --> Security & Privacy
Show the following:
Remote Management: Allow incoming connections
ScreenSharing: Allow incoming connections
Tested with 13 different MacBook Pros (15", 13", 2015, 2013, etc.) and all running macOS Sierra 10.12.3 - not working. Some of these MacBook Pros are brand new, straight from Apple (I run an IT shop).
Network tested on 4 different routers (home network with Orbi and Netgear, corporate network with Meraki devices, satellite office with Cisco network gear).
Apple Store Genius can't figure it out and have the "Have you tried reinstalling the os?" recommendation. Yeah, not a good recommendation given the above.
So it's not the network, it's not the computer, it has to be macOS Sierra.
BTW, I tried Parallel Access and it work just fine. I can access the folder and do remote screen sharing.