There is no way to force them to use them, they will just use them on their own until their stock you give them when you send them out goes away.
Nothing (that is in the game right now) can cause them to die in a single attack that they would not be able to heal from so no worries there. When they get up to the radiation amount a RadAway would heal then they will use one, then their health is low enough for a Stimpack to fill it up, they will use it.
A good ratio is 2 to 1 from Stimpacks to Radaway. I generally will send out my guys with 20 Stim Packs and 10 Rad Aways though they will often still return with a RadAway or two on them. I will also do 15 and 10 if I am low. Your residents will never need RadAway unless you run low on water so as long as that is ok do not fear sending more with your guys in the wastes.
Results from the wasteland are mostly random. It is highly unlikely (but not impossible, as you have the proof in your game) that a level one dweller with wimpy stats comes across the most powerful weapon in the game in an hour of exploration. Your badass explorer with top stats and elite gear might not see that type of weapon after exploring for a week. This is how the RNG works.
Because of the randomness, there is no formula that guarantees that a dweller with X stats and Y gear explore for Z time period will come back with the best loot. What we do know is that having better SPECIAL, a higher level, and exploring for longer periods of time make it more likely that the dweller finds better gear, more caps, and earns more experience than another dweller with lower stats exploring for a shorter time period finds. You can see this at work by looking at the results after multiple explorations. Jericho may not be bringing back plasma weapons and fat men every time, but he should be reliably finding shotguns, rifles, and the like rather than rusty pistols.
The other factor that you haven't mentioned with Jericho is his level. Results in my game suggest that the level of the explorer may also factor into the quality of loot they find (although part of this is that lower level wanderers just can't survive very long). My lower level explorers tend to find mostly pistols, maybe
tl;dr
Yes it's possible. Congrats on your guided fat man. With repeated expeditions, the results should be more in line of better stats + more time = better loot, but there is no surefire way of getting the absolute best loot every time. Improve your SPECIAL, improve your level, send out for as long as possible, pray to the RNGods, and send more expeditions. Eventually you will get what you are looking for.
Best Answer
The following is largely taken as is from Google Docs "Fallout Shelter Efficiency Data"
I do not know the authours or contributors of this document in any way.
The in-game guide states "The further out they go, the better rewards they'll find, but the harder the encounters will become"
This infers that as the probability of loot being rare/legendary increasing with time.
A regular loot event occurs every 60 minutes for all dwellers exploring in the wastelands. This is confirmed to have a chance to acquire rare and legendary gear. Only Legendary weapons have been gained this way, not armour.
Rare drops after 25 days in the wastes are confirmed to be 100%.
Also, when your dweller reaches 60 hours (plus or minus 15 minutes), they will encounter the National Guard Depot. This will always happen. However, you do not always gain the legendary gear. It is suggested that this is based on a Perception test, but this is not confirmed.
In conclusion:
If you are looking for Legendary gear, stay out there as long as possible, but consider coming back as soon as you have one.
If you are are okay with only 1 piece of Legendary equipment per expedition, stay out as long as possible and collect as much better-than-common gear as possible. And if you find that you can indeed gain more than 1 Legendary gear, then by all means share that information.