Even though you can't use WIFI at work (and even if there isn't a WIFI location anywhere), Verizon's WIFI Auto-on will STILL turn on WIFI if you set work as a location. It doesn't matter that there isn't WIFI, all Verizon WIFI Auto-on is doing is determining your location using the Cell sites to triangulate you, and then turning on the WIFI radio at those locations you specify.
You don't NEED WIFI available for the Verizon app to work, but you DO need WIFI ON for Smart Actions Location triggers to work. So instead of the timeframe as you've set, you can replace that with the Smart Actions Location trigger instead and all will work fine.