I’ve just spent some time trying out how Cadence behaves when it comes to the charges and dual wielding guns and have arrived at these conclusions.
If you attack with both guns on the Cadence hit (33% chance of occurring), you will only need one attack after that for another Cadence hit. In this case (attack with both guns), the first of the 2 attacks (main hand) will be the Cadence hit, the other (off-hand) will be a normal attack that can trigger any WPS. So if for example Storm Spread procs on that attack, you will simultaneously attack with Cadence by main hand and Storm Spread for the off-hand AND will need only one attack to charge the next Cadence.
Note that if the attack with both guns procs at any other point than the actual Cadence attack, it only counts as 1 charge.
WPS that make you shoot 4 times while dual wielding (Volley, Chilling Rounds etc.) grant 2 charges IF you are at 0. So say you are at 0 Cadence charges and your first attack is a Volley from Gunslinger Talisman - next attack will be Cadence. This is probably the only WPS type you should run with Cadence as it can allow you to trigger it more often. When they trigger right after your last Cadence attack which only used one gun, it allows you to skip a charge. Not sure if there is a list of WPS that make you shoot 4 times, I only tested with the 2 above.
Seemed chaotic at first but after spending a lot of time just shooting the dummy and observing the behavior, this is how it seems to be. No WPS besides those that fire the 4 shot salvos allowed me to double charge Cadence (even those that attack with both guns) and there is a 33% chance of needing only 1 attack for the next Cadence (if the 33% chance to fire both guns procs on the actual Cadence hit).