All gelling agents work only under certain conditions. You need to be in the working range for:
- temperature
- sugar content
- pH
- alcohol
Pectins are more sensitive than gelatine, working in narrower ranges. Also, not every pectin is active in the same range, the main difference is between HM and LM pectin.
You can try if gelatine works with your recipe, but here we get into shelf life problems. If you wanted a refrigerated jelly, gelatine is OK. But if you want a jelly that is shelf stable after canning, you need to have at least 33% sugar by weight, better more, and as far as I know, it won't work with gelatine (I don't know if this is because of food safety consideration or because this is outside of the gelatine's working range).
The better way is to find out what changes to make to the recipe in order to have the proper ranges for pectin to work. Use this table for the pectin properties.
(source: Texture by Martin Lersch)
If your pectin type was not on the label, you're more likely to have HM pectin.
I don't know whether trying to reprocess your current batch of jelly is worth it; it may or may not work. You have to calculate the risk (do you see it violating some of the conditions on this table?), your time, and the cost of the ingredients. Also, you don't say how much sugar you used, but if it was too little, it is not edible after 2 weeks in the fridge.
Pectin needs acid to work. Fruit never has the same amount of acid. Not only do blackberries have much more acid than apricots, but two different cultivars of apricots and even two apricots of the same cultivar but grown in different conditions will have a large difference in the amount of acid. Ditto for lemons.
Your fix proves that this is the reason - once you added more acid (in the form of lemon juice), the problem disappeared. So, the reason "why" is simply "you didn't have enough acid in your jam".
The question of "why would the company publish a recipe" - it publishes a recipe which works on average, but it can't make a recipe which works for all fruit grown under all conditions. I can't tell you why your fruit is lower in acid than average (although the amount of sunny days during ripening is probably involved) but it seems that it is.
Best Answer
You can use a chilled plate to test your batch before canning it next time. Pectin does not firms up with time, just temperature.
I would suspect that the watermelon juice has made your jelly too dilute, and you'll need to boil your jelly down further.