My wife and I received our cards at the beginning of July. We have been using it mainly for groceries. The Synchrony Bank website keeps track of the purchases and the Verizon Dollars. So far our account shows no Verizon Dollars.
The Verizon Visa Card website states it can take 1-2 billing cycles before they appear. The credit card purchases post within a couple of days. I don't see why the same can't be done with the Verizon Dollars instead of having to wait for 1-2 billing cycles.