Well, stuff that you implicitly learn are things that you cannot 'explain'. In the paper, they say they use sequence learning as their implicit learning task. In sequence learning, you show some visual stimuli, and the subject reacts. Depending on the test, the sequence may have underlying structure. I don't have access to the paper, so I'm speculating here, but its probable that they used a test with underlying structure, and measured the reaction times of the subjects. This test essentially tests the subjects 'subconscious' pattern recognition. And one of the hallmarks of implicit learning is that your skill is only weakly transferable to other skills. So it might be that only sequence learning is impaired by mindfullness. Who knows.
As for if implicit learning is 'bad'? Well, it certainly depends on context. There are definitely large areas where it is preferable to have explicit knowledge. That said, there are also lots of situation where it simply isn't feasible to get that explicit knowledge - we must fall back to implicit learning. For example, language learning is a pretty weird case. As children, language learning is pretty much mostly implicit - it is entirely possible to develop into a passable English speaker without being to articulate any of the grammer rules. Even as adults, we are often told to stop worrying about the rules, and just get exposure to the language - this too relates to implicit learning.
The way you describe it, implicit learning is the formation of associations, pattern matching, and what some call intuition. I've seen great things done with fact-based x-causes-y deduction as well as intuitive understanding that is hard to explain. I've also seen cases of each where a person who thinks the other way would never have found a solution to a problem. I would not discount implicit learning, nor promote it as "better".
Are we getting at the old right-brain left-brain thing here?
Implicit or procedural learning refers to learning how to do things like tying your shoes: It requires considerable cognitive effort and attentive control of muscles to get right, but eventually, after you've done it many times, you don't think about it anymore.
Driving is another example: After sufficient experience, you drive without conscious effort, becoming consciously aware of things only when they exceed your implicit bounds ("That car is too close, what's that unexpected shape at the side of the road").
The basic gist of the article is that mindfulness (which essentially makes you both more aware of and detached from your conscious cognitive efforts) mixes poorly with learning tasks or activities that are intended to eventually be performed automagically.
I suppose, I speculate, that the reason for this is that implicit learning requires you be "all in" attending to the task, but mindfulness would have you at least partially attending to your attention, so your mind is in fact distracting itself.
I further speculate that this likely "weakens" the "signal" your brain is trying to send from the explicitly conscious regions of your brain that are attending to the new task to the implicit, subconscious regions that will eventually perform the task, once it has been well learned.
(Just for fun, try to describe to someone in step-by-step detail how you tie your shoes. Then try tying them while describing what you are doing. Report back on how many attempts it takes before you succeed.)
I tried very hard for a long time to explain to my daughter how to make herself go on a swing with no luck. "Lean back, legs out, when going forward..." Then I sat on the swing next to her and did it myself. She watched and was doing it herself in about 5 seconds. No idea if anything I had said helped prepare for that. I think she had seen me swing myself before and didn't get it, so IDK what clicked.
The full paper is linked here in a toplevel comment. It seems like speculation is unproductive, because the paper is highly technical and has particular definitions for all of its terms. Without reading the paper it'd be hard to know what they're talking about.
As for if implicit learning is 'bad'? Well, it certainly depends on context. There are definitely large areas where it is preferable to have explicit knowledge. That said, there are also lots of situation where it simply isn't feasible to get that explicit knowledge - we must fall back to implicit learning. For example, language learning is a pretty weird case. As children, language learning is pretty much mostly implicit - it is entirely possible to develop into a passable English speaker without being to articulate any of the grammer rules. Even as adults, we are often told to stop worrying about the rules, and just get exposure to the language - this too relates to implicit learning.