That wiki page covers two aspects of the trials. The first is the reward system that gives you items based on a percentage chance, which is based off the difficulty of a given trial. The second are achievements related to having the trials active.
Let's just take the achievement Trial of the Fool, which is gained on reaching Skyhold at level 5 or less. This achievement is used in coordination with the Take It Slow trial, which cuts XP gains by half. If you are only using trials for the achievements, you turn it on, and then off again when you have the achievement. The descriptions on the trials page under Hints and Tips are about gaining the achievement, NOT about the rewards.
For the rewards, each individual trial increases your chance of getting a reward, with some giving a higher chance than others.
* * *
I'll give some examples. These are made up numbers, since I don't know the actual percentage.
Even Ground - Enemies always scale to be at least the same level as the Inquisitor. Significantly increases the chance of receiving special shipment rewards in your stronghold.
Walk Softly - The enemies of the Inquisitor may have new traits and abilities in combat. Significantly increases the chance of receiving special shipment rewards in your stronghold.
* Rub Some Dirt on It - All healing potions heal only 1 health. Significantly increases the chance of receiving special shipment rewards in your stronghold.
Grizzly End - You thought bears were tough? Think again. Significantly increases the chance of receiving special shipment rewards in your stronghold.
* Travel Light - All supply caches are removed from the game. Slightly increases the chance of receiving special shipment rewards in your stronghold.
* Rest Easy - You lose all focus if you rest or travel to a camp. Slightly increases the chance of receiving special shipment rewards in your stronghold.
* Take It Slow - You gain XP at half the normal rate. Slightly increases the chance of receiving special shipment rewards in your stronghold.
Fair-Weather Friends - Negative approval changes for followers are doubled. Slightly increases the chance of receiving special shipment rewards in your stronghold.
So, for the sake of this example, let's say that the "significant" chance increase is 10%, and the "slight" chance is 5%.
if you add all of those up -- (10x4) + (5x4) = 40+20 = 60. That is a 60% chance total to get a reward if you have ALL of the trials turned on.
Now, if you're like me and not interested in a challenge, or achievements, but only want items, you may turn on some of the easier ones, like Rub Some Dirt on It (potions heal 1 health), Travel Light (no supply caches in dungeons), Rest Easy (focus resets on traveling to a camp), Take It Slow (half XP gain). Playing in casual mode also helps. That is 1 "significantly" and 3 "slightly," which would be a total of 25% chance to gain a reward with that selection of trials.
I think that Travel Light may only apply in dungeons, as there are no supply caches in the outside world, so that 5% may not be active while out exploring. In addition, you do have to be out in the world exploring and also fighting. You don't get anything while just standing around in a camp.
One final tip is that you can "save scum" if you're looking for a specific item. If you want, say, the Armada Captain's Knife Schematic, once you have a reward available, you can stand in front of the chest, do a save (a hard save by going to the menu and hitting "save," OR a quick save), and open the chest to obtain the reward. If it's not the thing you want, then you just load up your save, re-open the chest, and continue to repeat this until you get your desired item.
Also, keep in mind that there is a level division. There is an initial grouping of items that will change on reaching level 13, so be sure to collect the things you want, save scumming if necessary, before level 13. After that point, there is a new selection of items available.
You sure they weren't DLC items, like Flames of the Inquisition items? I've only ever got one special delivery at a time. Although I suppose if you don't pick it up right way, maybe it stays there and you might earn a second one? I never wanted to risk it, always try to pick it up as soon as I earn it.
They will just accumulate until you pick them up. On one occasion I got two reward messages while out exploring and they were both waiting for me when I got back.