Most of these tamers are always available to challenge, not only when their world quest is active, and you can challenge them repeatedly. You can find maps on where to find each of these tamers by visiting their specific section and hovering over the map symbol next to the coordinates.
This can be especially useful if you are aiming to complete the achievement Family Exorcist for which you need to defeat tamers with teams made of pets from specific families only. Strategies for all those combinatins are available in the Family Exorcist section.
Another interesting piece of information, thanks to Valinrista#2543 for the heads-up: these world quests can be done once per character, instead of once per account, as was the case in previous expansions. This can be useful to farm pet charms at the same time as ticking off some family achievements, if you don't mind logging around a few characters.
Xu-Fu can scan this section for the most suitable strategies according to your preferences and show the required pets.
Depending on the amount of fights in the section, this can take up to a minute to process.