It sounds like you didn't use pure gelatine, but a pre-mixed product. The way you describe it - with sections which are set and sections still liquid - it sounds like a clumping problem to me. The very weird directions you mention increase my suspicion.
Normally, if you put dry gelatine in hot water, parts of it will change immediately, while parts will stay dry. This is why you bloom gelatine in cold water until it is thoroughly hydrated, and then gently melt it on low heat. Too much heat will inhibit setting. I suppose that the mix manufacturer created finer-ground gelatine powder than usual and mixed it with something else, probably dextrose, to ensure immediate dispersion and hydration without clumping, and it probably works well enough in most cases.
There are several things which can have gone wrong for you. Maybe your pyrex bowl didn't have enough thermal mass to cool the water enough before you added the package and the gelatine got slightly overheated. Maybe you had stored the package not dry enough, so the dextrose clumped during storage and now the gelatine wasn't dispersed, so it stayed in chunks after hitting the water. Maybe you didn't stir it well enough to mix it evenly. Or something else entirely - the directions don't seem like the best way to handle gelatine.
You can try to save the next package.
I would start with letting the water cool just a little bit before stirring in the jello, maybe 75 or 80°C. Then I would take a good look at the package content. If there are clumps in it, there is a good chance it won't work properly. I don't know what will help in this case, maybe putting it through a food processor. (Just sieving out the clumps is not good; you may be throwing away the gelatine and keeping the dextrose). Then I would try to give it a really good and thorough stir before adding the cold water, so everything is perfectly dissolved, and another thorough stir after the cold water, so it is the same temperature and concentration everywhere.
I can't promise that this will help (I may have made false assumptions here, never having used a package of premixed jello), but it seems the likeliest solution.
Update Kristina Lopez says that lower initial temperature won't work with jello. I proposed this because gelatine is succeptible to overheating, but didn't consider that maybe starting from lower temperature will prevent sufficient dissolving once the cold liquid is stirred in. I guess you could still try out different heating startegies, but if somebody can predict how they'll turn out, it's not me, obviously my experience with pure gelatine is not sufficient here. So I'm striking that part of the answer and leaving in the break-up-clumps suggestion, as this is a thing I am more certain of. (I have had this problem with mixes of other gelling agents, for example jam sugar).