Not necessarily. The agent versions do need to match throughout the product, especially from version 4.11.x to 4.12.x. So, as long as you are matching, you should be fine.
Without looking at it, I'm thinking that the agent may not be pointed to the Profiler server correctly. To verify, click on the traffic light icon again (and get the error, again). Once you do that, go to the agent and look at the Kernel.log file in the agent's install directory. At the bottom, if there is -some- kind of communication, you should see an "incoming GET request from xxx.xxx.xxx.xxx" (where the x's are the ip address of the Profiler Server). Make sure that ip address matches what is in the core.xml file (in the same location as the Kernel logs)
If you don't see that message, make sure you can ping the Profiler Server from the agent. Also make sure that all firewalls are open between agent/server on ports 162 and 4319.
Let me know if this helps.