One thing that hasn't really been addressed here is the question in the title of the thread.
It's worth understanding that diesel fuel and the exhaust from a diesel engine are two quite different problems.
The fuel is oily and, depending on the grade used, potentially quite smelly. If you spray it about, droplets of liquid are inclined to stick to surfaces and then evaporate slowly, so it stays noticeable for a long time. I suspect this is what gives rise to the "several hours to several days" you've read about.
The exhaust from burning diesel is different: It varies a bit depending on how modern the engine is and the grade of fuel (especially the sulphur content) that's being burnt, but you're looking at five different groups of constituents:
First, and by far the greatest proportion, is hot air mixed with water vapour. The water vapour may condense out into a white cloud downwind of the exhaust, that then re-evaporates. All this is harmless.
The second, and this is unavoidable, is CO2. There will be a lot of this when the machine is running, though it will dilute in the wind on its way over the fence. As a simple gas, it will clear from inside your property as quickly as you ventilate the place with clean air. If you measure high levels of CO2 inside your property, it's as likely to have been breathed out by the occupants as to have come in from outside - it's not unusual to find CO2 levels of 1000 ppm inside an office space (compared to 400 ppm outside). Not really harmful at those levels - in the UK, the 8 hour occupational exposure limit is 5000 ppm.
Third is a collection of trace gases. Primarily SOx, NOx and CO. How much of each of these you get depends on the quality of the fuel and the design of the engine and its exhaust system. Like CO2, they will dilute a bit in the wind and will clear quickly with ventilation. SOx makes the exhaust smelly, is driven by fuel quality and can be associated with particulate problems (see below). In larger quantities, NOx is the stuff that makes your eyes water and CO is responsible for the headaches Bill was talking about. At that sort of level, they're unpleasant but the symptoms resolve when you remove the contaminant. At much higher levels (and you might achieve this by breathing pure, undiluted, exhaust), CO can kill you quite quickly.
Next and, with a modern, properly maintained engine and suitable fuel you should really see almost none of this, is unburnt fuel and soot. If you get this, it does have the potential to stick to surfaces and to hang about a bit. Distinct from condensed water vapour, this takes the form of smelly blue or black smoke. Anything beyond a quick puff at startup suggests a machine that isn't in a fit state to minimise any of the other contaminants either.
The other one to be aware of is particulate (you may see it referred to as PM10 or PM2.5) In many respects, this is quite like the trace gases - it will dilute and ventilate quickly. Modern engines with modern exhaust systems burning low-sulphur fuels generate a lot less particulate than traditional diesels. The health effects of inhaling particulates are much less immediate than the other contaminants, but much more likely to be long-term and cumulative. On this side of the Atlantic, a growing perception of the health problems caused by particulates has reversed what was a popular trend towards driving diesel cars. This might well be the element you want to pay most attention to.
Worth highlighting the importance of dilution. The key thing is what enters your property rather than what comes out the exhaust. How quickly and thoroughly the exhaust gases get diluted depends on a few things - including the design of the outlet and the temperature of the exhaust plume (the high temperature actually works in your favour) as well as the wind. The plume won't be at anything like 888F by the time it reaches your wall - but you ought to bear in mind that the strong westerly wind you mention is your friend; if you're going to have problems, they will be at their worst on days when there is no wind to help dilute the exhaust. If you get air-quality monitoring done, ensure at least some of it is arranged for a day when no wind is forecast.