Rare monsters in PSU are actually using a system that's not focused on them. If you look at missions, they tend to fall into 3 categories:
1. Missions that never have rare monsters, missions that always have rare monsters (these are fairly equivalent, really).
2. Missions with multiple sets with random rare monsters (ex: Citadel of Sand).
3. Missions with a single set with random rare monsters (ex: Fantastic Voyage).
Note that I said "set" there. I can't remember if I've really discussed mission organization here before, but...
In the spawn chart for Citadel of Sand, you'll notice there are 3 map layouts, A ("Stairs straight ahead"), B ("Stairs to the right"), and C ("Stairs to the left"). These are actually separate missions entirely, when you enter the counter, the game randomly chooses which one to display (usually it's just a "generate a random number between 0 and 2, if it's 0, give the first layout, if it's 1, give the second, if it's 2, give the third"), but each one has the same name/description/rewards so they can keep it secret.
Within each map layout, there are 3 enemy lists. Each one of these is a "set" (a set contains listings for all the objects, enemies, etc that appear in a given mission); missions can have between 1 and (unknown; you tend to not see above 4, but there's no guarantee that this is the actual limit) sets, chosen randomly, weighted however Sega saw fit. A rare monster layout is merely any set that has rare monsters placed in it (they're treated like normal monsters).
Online v1 free missions and offline AotI free missions all fell into category 2, with a 33/33/33/1 distribution on set choices. Online AotI free missions tended to be category 2 with a 32/32/31/5 distribution, while a few post-third-update ones were category 3 with 90/10. Events were a mixed bag--Ark to the Future had guaranteed rare monsters and instead used sets to determine where the chips were hidden, while Maximum Attack G had two different sets with rare monsters (the final block could have Gaozorans, Delnadians, or Rappies; nothing else in the mission changes).
(I've considered trying to add a PSO/PSO2-esque "any monster in a certain species can generate as its rare equivalent", but that seems... a bit unlikely. Suppose I should map out what I've thought about doing, categorized in terms of plausibility, at some point.)