The iPhone is functioning correctly. You have AT&T set for voice and Verizon set for Data. Both will work perfectly while the iPhone is in Stand-by mode. When you make a voice call on AT&T, then the iPhone works in a single SIM active mode. In other words, once voice is active on a particular SIM, then the other SIM becomes inactive (Unless you are connected to a Wi-Fi Network, then data will work with the voice SIM).
So, In your example, Once AT&T is active on voice, then Verizon will be inactive on data.
NOTE: In your setting if you make a call on the Verizon line, then AT&T will be inactive but you will also have data since data is assigned to the Verizon line.
Axel F.