After adding a device that is seen and is functional in the Alexa app - it can sometimes be hours, or a day before that device shows up in the Hubitat app.
If even possible (I don't know if it's a push, or a pull thing!) can there be a 'force update' button type thing added?
Help us understand a little more, please.
If this an existing Hubitat Device that you have exposed to the Amazon Alexa app via Hubitat's built-in Amazon Echo Skill app?
Which Hubitat "app" are you referring to? Are you referring to the Hubitat Mobile Phone App running on your smartphone or tablet?
The confusion arises as your fist statement could be interpreted to mean that you added a smart home device directly to your Alexa mobile phone app, without any Hubitat involvement whatsoever. In that case, until the device is manually added directly to Hubitat, it will not be visible in Hubitat via the HE hub's web front end, or the HE mobile phone app. The built-in Hubitat to Alexa integration is one-way, sharing existing Hubitat devices (e.g. switches, contact sensors, locks, dimmers) from Hubitat to Alexa.
Or...are you using the community developed Echo Speaks integration? This allows Amazon Echo devices to show up in Hubitat as speaker devices. Perhaps this is what you're asking about?
Yep - needed more details.
I'l give you a real world example that I just went through that prompted the question!
Picked up a Tuya Zigbee tap switch.
Added it to the Tuya app.
Alexa then found it on its own shortly after (got a pop up on my phone).
Tested it there, and the Zigbee device will trigger an on/off indication in the Alexa app on the phone.
Went into Hubitats interface
Apps
Amazon Echo Skill
Did the usual things that we all know
No (new) device found. Even tried restarting Hubitat to see if that would force it to look for new devices (nope). Then thought... hey! we need a button. Or something. 
And here we all are.
The Amazon Echo App only exposes Hubitat devices to Alexa, it doesn't pull in Alexa devices to Hubitat. That is why so many people have various methods of controlling Alexa devices from Hubitat, like using a virtual contact sensor and an Alexa Routine.
That is 100% the expected behavior. Alexa-connected smart home devices cannot be shared with Hubitat via the Hubitat Amazon Alexa Skill. As previously mentioned, the built-in Hubitat Amazon Echo Skill integration allows for one-way sharing of devices, from Hubitat to Amazon Alexa.
From the Hubitat Documentation
You sure its Zigbee? You cannot pair a zigbee device directly to a mobile app, unless you also have a separate Zigbee hub? It sounds like a Wifi device you added to your Wifi via the mobile app?
If it is Zigbee, you should reset it and pair it directly to Hubitat.
Download the Hubitat app
