(Disclaimer: I have not read the article (or if I have it's been a while and I've forgotten what it said). Also, I do not consider myself an expert at Procession but the following is my experience with it.)
Procession is not a Throne Room variant. It's a trash-for-benefit card, with the benefit of playing an action card twice before you trash it. If you try to use it as a substitute for Throne Room, or for a similar function to Throne Room, the result will be disastrous. You'll end up with too many power terminals and not enough villages, or too many villages with no terminals, or just a bunch of random action cards you didn't want. When you pick up Procession, it should be because you're thinking "I want to upgrade my actions" and "I can easily replenish the cheap pieces of my deck". And when you play it, it should be because you're either done with or can replace the card you're trashing, and because you want an action card costing exactly $1 more than it (or if it is the late game and you're ready to cannibalize your deck). On boards where you can easily control how many of which engine pieces are in your deck at any given time, Procession is incredible, because not only does it increases the overall "value" of engine pieces in your deck, while throning cards as they start losing utility. So, how do you identify a good board for Procession? You want the following things:
1. Gainers (especially Rogue and Graverobber). The combo with Rogue/Graverobber is obvious: trash good cards with Procession, and then dig them back out of the trash with Rogue or Graverobber (and even top-deck them in the latter case). But even aside from these two cards, gainers are huge for Procession. They help you pick up cheap engine parts to upgrade, and when you think you're closing in on the mid-late game, you can Procession those gainers in one final hurrah to grab two more cheap engine parts and $4/$5/$6 (depending on the gainer).
2. Strong trashing. Trashing helps you maintain solid control over what is going into your deck. In a thin deck it's easy to check "I have too many terminals" or "I don't need this many villages"; great, upgrade them with Procession into the terminals/villages that you need.
3. +Buy. Similar to the point with gainers above, you usually want to be picking up cheap engine pieces quickly, and +buy can help out with that a lot.
4. Combos. As with all TfB cards, you should look for on-trash bonuses. Fortress may be the most obvious, but getting a Duchy as compensation for a late game Hunting Grounds popping, or extra Processions (or other cheap engine pieces) for trashing Catacombs, or extra attacks from Squire, etc. can be great as well. One-shots are also awesome with Procession, even more so than with TR, because you get an extra benefit for them. Processioning Feast for three $5's actually makes you want to go for Feast (and maybe even pick one up as one of your three $5 gains!) (warning: only do this if you're sure you can actually connect Procession with Feast), and Processioning Pillage for an extra two Spoils and a $6 is a nice bonus. Knights also have a semi-one-shot aspect to them, so Processioning them can be nice if they would have died after the first hit anyway. (In particular, Processioning Sir Martin can pick up another knight!)
The following things should trigger a red flag in your head that says "Don't get Procession":
1. A lack of a strong sequence of action cards at consecutive costs that you want. There should almost certainly be at least a $3, a $4, and a $5 that you want. Procession is probably that $4 if you want to use circular reasoning, but still check for a $3 and a $5 which you want. If these are not present, you probably don't actually want to "upgrade" many of the actions in your deck, and so Procession's main benefit is negated. Ideally there will also be at least either a $2 or a $6 that you want. The point is, it may be a strong engine board that has the stuff mentioned above, but if all of the good engine components cost exactly $5, or exactly $4, or whatever, then you aren't going to be getting them by trashing stuff costing $1 less, since you don't have stuff costing $1 less. You also usually want a good $4 alternative so that you don't always have to get Procession after trashing your $3's, but it's not necessary; just be prepared to play Procession a lot (meaning you'll also be grabbing lots of $5's), so get lots of cheap fuel to upgrade quickly.
2. Junking attacks (that can't be easily overcome with strong trashing). If you can't consistently connect Procession with action cards you want to trash, then Procession will often just be a dead card in your deck, and you don't want to pay $4 for that! On the other hand, you can use Procession to trash Ruins with a minor benefit, but this is generally weak and slow, and you should have a good reason for thinking it's okay before you go for it. (Example of when it might be okay: you would otherwise want Procession, you have fast treasure-specific trashing with Spice Merchants, and you can build an engine if you can clear out your deck; then Processioning Ruins may be a good way to get there.)
Other types of attacks might also be bad for Procession, I don't really know about that. Anyone else want to comment on it?
I want to give an example game, but I can't find the log I wanted to use. I think this game was from summer 2013? So I'm really re-constructing this from memory, but I remember it pretty distinctly, since it was the first time I saw Procession shine. The board was: Chapel, (some good $3), Procession, Bridge, Monument, Laboratory, Rogue, Grand Market, King's Court, shoot that's only nine cards. Maybe another $3 or something that just didn't get bought. I can't remember what the good $3 was but I remember it being something you didn't mind having, though it wasn't something you needed either.
Okay, so I opened $2/$5 in this game, which is amazing. Ultimately it was just a race to set up KC-KC-Bridge-Bridge-Bridge, but Procession was essential to getting there. You trash down with Chapel, then on your last time playing it Procession it to grab the $3 and get it out of your deck. Pick up lots of $3's, Bridges, and Processions, so that you can buy lots of cheap engine parts (from bridges), and upgrade stuff quickly with Procession, picking up Rogues, processioning them into GM's (to circumvent the no-Copper restriction, though you probably don't have any Copper anyway), and grabbing your good cards back out of the trash. Eventually you can Procession GM's into KC, and you'll reach KC-KC-Bridge-Bridge-Bridge and win.
So the following things make this nearly the optimal Procession board:
1. Strong trashing from Chapel
2. Rogue to dig stuff out of the trash after you Procession it
3. Bridge for awesome +buy that can pick up lots of cheap components fast
4. A clear chain of cards costing from $2 to $7, with at least one that you want at each price
It's also worth noting that if you play Bridge enough times in a turn, you can Procession "cheaper" $0's into $1's (like Chapel into KC as an extreme example), but that's not a big deal, it's unlikely to come up many times before the game ends.
Hope that helps! I am also completely open to hearing more experienced players' comments/corrections to my thoughts.
