@JoaoGabrielMoraes, I feel like you're asking two different questions here, and I can only answer the first one confidently 
1. I'm feeling good here...
This is covered in the docs:
adapter is the "Sequence of an adapter ligated to the 3' end" of whichever read is specified in the parameter (e.g. --p-adapter-f is the sequence of an adapter ligated to the 3` end of the forward read)
front is the "Sequence of an adapter ligated to the 5' end" of whichever read is specified in the parameter.
The cutadapt docs go into depth about the various ways these and other parameters can be used to describe different barcode/primer placements.
2. Please take this attempt at an answer with a grain of salt.
I suspect your colleague went about things the right way, but I'm not sure my understanding of how forward and reverse reads work is correct. I'm imagining a matched pair of reads looks like this...
(5') 515primer->fwd-sequence->index (3') ...... (3') index<-rev-sequence<-806primer (5')
... so both primers get assigned to front parameters, while the 3' ends are on the "inside" and are assigned to adapter.
Does this line up with your understanding of the sequencing process? Does this make sense?
Best,
Chris 