Poor honing on a blade that was already in true can reduce the sharpness, as you have discovered. This happens if your angle is off, and you knock the edge of the microscopic burrs or teeth over, presenting a duller cutting surface.
It is likely that proper honing will correct this, although it may never be quite as perfect as the blade fresh from the whetstone or factory.
In any case, you will not do any permanent harm to your blade with a honing steel (short of using it as a bludgeon), because absolute worst case, you can always have your knife resharpened, or do it yourself. This may be somewhat inconvenient or costly, but is much less expensive than replacing a blade.
Your link has directions for use: "To properly hone the knife, hold it at a 20-degree angle and draw the blade across the steel. Never stroke the same side of blade more than once in succession."
In general, ceramic rods are more forgiving than the grooved steel ones -- which, in my opinion, should be avoided on good knives. (But that's another discussion.)
The primary purpose of a honing rod (of whatever composition) is to straighten the edge, not "sharpen" it. Polished smooth steel rods are useful for that purpose, but many people have found that ceramic rods have enough abrasiveness to smooth the edge very slightly while also straightening it. (They are also useful for deburring after sharpening with a stone.)
Generally speaking, you'll want to use your ceramic rod at a slightly wider angle than the edge of the knife. Global knives probably have a steeper angle on their edges than, say, traditional German knives: they're probably something like 15 degrees, so the recommended 20 degrees in your link instructions is probably about right, though slightly wide. If you don't know how big 20 degrees is, look at a protractor. With a honing ceramic, you're not going to ruin your edge with a few light strokes, so try your best to maintain that 20-ish degree angle in just a few long strokes alternating sides. (Do NOT do like the chefs do on TV with a grooved steel and rapidly stroke the blade dozens of times -- it's probably better to do a touch-up with a ceramic rod with just a few slow even light strokes on each side periodically as needed. You should be able to feel the difference in the edge.)
If you know what you're doing and are sharpening your knives yourself, you may find on Globals that a slightly steeper angle (e.g., 15-18 degrees) for honing gives better results in terms of maintaining the edge longer between sharpenings by keeping a more consistent bevel. But it really depends on your maintenance schedule, angle you use to sharpen, and how hard you use your knives.
If you are inexperienced with honing knives in general, though, I'd highly recommend just talking to someone who knows what they are doing. It's nearly impossible to describe good technique briefly in writing.
Best Answer
I have a very simple reason for taking the edge away: It's less dangerous - for you, don't do this before someone.
I don't know if it makes for better or worse honing (should be the same as long as the angle is the same I'd say).