AMF's typical schedule is an early AM show, fly to an outstation, layover for 4-10 hrs (varies greatly between runs around the system), then fly back to the base town in the PM. This is the typical "feeder" schedule that most of AMF's bank and UPS runs subscribe to.
The most common AMF run services UPS and the "feeder" schedule services their big jets. In the AM, UPS's jet will fly into the big base city with cargo for AMFers. AMF's will load up and take this cargo out to smaller outstation cities and then stay there until the evening. In the PM, after all the UPS pickups have occurred in the small cities, the drivers will bring the cargo out to the airport, load you up, and you will fly the cargo back to the big city that evening. Once you get there, they will take your cargo, load up the big jet, and it'll fly into SDF to be sorted and the whole process starts all over again the next day. The biggest variable in the schedule is when the jets you are providing service for are scheduled to arrive / depart the base cities. This will determine your show times, layover times, etc.
Some runs with extremely long layovers will require you to get rest in the outstation city during the day and you are technically "on-duty" overnight. Some runs also provide Saturday service to some outstations that require the airplane to stay in the outstation over the weekend. Most of these runs are what AMFers call "outstations" where the pilot actually lives in the outstation town instead of the base city.
As to the rest issue, I have NEVER had a problem with rest rules at AMF whatsoever. When assigned a trip with a 91 leg that will exceed your duty/flight time limitations, if it is going OUT to PICKUP cargo, that is considered duty and cannot exceed FAR limitations. If the 91 leg is to return to the pilot's home ("tail end" 91 leg), then that is legal ONLY if (1) you are ok with it and (2) with the permission of the Chief Pilot / VP Flight Ops. This does happen from time to time and some schedules do have a built in 91 leg home however, THE COMPANY CANNOT ASSIGN YOU THIS LEG...it is only IF YOU WANT TO OR NOT and if can only be a 91 leg back to the pilot's home (domicile) The company cannot force you to do it. This is explicitly outlined in the company's procedures. Some schedules that have this type of leg over and over will show it as part of the scheduled run but they CANNOT ASSIGN YOU TO DO IT if you are over your duty requirements.
Again, as a former AMF pilot, I have never had any intentional company-related problems with rest/duty rules. If you know the rules and say something if you see a problem, you will never have a problem. Sometimes a scheduling error will occur or a dispatcher might not know the rules you are governed by to the T but in the end, you are the responsible party anyways so know the rules, and you'll be just fine.