Welcome to Hubitat!
Both Amazon Alexa and Google Assistant are primarily one way devices. You use Voice Control, or Routines, on these two platforms to control the devices that are paired with your Hubitat Elevation Hub. You can choose which devices to share with Alexa for Google Assistant as you see fit.
Currently, neither of the Hubitat integrations for these 2 voice assistants allows Hubitat to directly issue commands to the Alexa or Google ecosystems. These voice assistants expect users to issue voice commands, or to set up Alexa Routines/Google Assistant Routines, in order for anything to happen.
To get around this limitation, users will sometimes choose to set up the Google Assistant-Relay on a Raspberry Pi. It is not as hard as it seems, and you can follow my step by step guide that I wrote for myself (in the event I ever had to install it again! 
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So, why would you go through all this effort? Well, the one very cool thing about running an Assistant-Relay instance is that you can have Hubitat issue "spoken commands" (inaudible) to your Google Home platform.
For example, today you might say to Google Home something like "OK Google, set the Nest Thermostat to 73 degrees" (or whatever the right phrase is .) Since Google seems intent on not allowing other systems to control the Nest Thermostats directly, someday voice commands like this may be the only way to control a Nest T-Stat. What if your Hubitat hub could issue a text-based command like this to your Google Assistant? Well...enter Assistant-Relay with my Hubitat Driver. You can use something like Rule Machine to easily issue a custom command from Hubitat to Google by simply creating a RM Action to Speak the following phrase - "[CC]turn set the Nest Thermostat to 73 degrees". This will be completely silent, but Google will basically believe that you issued a voice command to control the thermostat.
Note: Not all commands will work correctly doing this, and none of us know if Google will eventually shut down this backdoor for controlling their system. We may end up having to have an Amazon Echo next to a Google Home so we can actually issue spoken voice commands from one system to another! Crazy as that sounds, some people have done it!
Hope this helps explain why you might want to tackle the Google Assistant Relay at some point in the future. It's not a trivial task to get up and running, but my MS-Word document has every steps detailed with screen captures. It is in the GitHub repo along with the groovy device driver.
