There are lots of different ways to do it with different results. What I want is for series mode to act like a single delay pedal, but with double the amount of time that a single PT chip can do. This means sending it through the delay chip, then sending that delayed signal through the second chip, but not using the output of the first chip directly.
Then, in parallel mode, they are totally separate chains until they mix at the end. This, combined with the cool ratio knob of the the PTAP, allows you to tap in a time, but have one delay repeat 3 times for every 4 repeats of the other - this makes for very interesting rhythmic possibilities. Or you can have one set to fast repeats and the other to repeat every fourth beat, the classic U2 Edge thing. Doing this requires separate feedback paths for the 2 delay chips.
The way BYOC has it on theirs, in parallel mode there's no feedback on one of the delay lines, and they sum together and get repeated through just one delay. If you listen to their clips you can hear what I'm talking about, but it's pretty limited. Totally reasonable to keep it simple since it's their only PT delay, but for my project I want to do something crazy and deluxe.