Congratulations on the new truck.
I saw a couple incorrect assumptions about DEF here. DEF is part of a SCR (Selective catalytic reduction): system, that is used in the exhaust stream to catalyze NOx (mono-nitrogen oxides) into water vapor. It has nothing to do with the DPF filters, they are 2 independant systems. Currently all DPF systems need to be burned off when they get full, this is usually done based on sensors that monitor pressure, flow, and a few other things in the filter, but is also done on a fixed mileage basis as well in the case of my '15 F350, I'm not aware if the other manufacturers do this. When the system determines it's time for a regeneration, it releases extra fuel into the exhaust stream by either pulsing the injectors again while the exhaust valves are open, or by the use of an additional injector in the exhaust manifold ala Chevy. This causes the temperature of the exhaust stream to rise dramatically, until it hits a temperature that causes the black carbon/soot trapped in the DPF to be burned off, and released from the tailpipe as a small amount of ash. When driving hard, or towing heavy loads, the system will experience "passive" regeneration, as the EGT's are high enough to cause the endothermic reaction in the DPF filter, but when doing lots of stop and go driving in city traffic, it builds up and then an "active" regeneration occurs.
Cheers