I see a lot of things online about the caffeine in tea and notice that many people are incorrectly informed about where the tea rates on a caffeine scale.
White tea actually has more caffeine per leaf than black tea due to how it is processed. However, once brewed, the reason the cup has less caffeine when brewed is because you steep it at a lower temperature (165F~185F)(73.8c~85c) for less time (1.5min~4min).
The rankings per cup are usually:
Pu'erh/Darks (Pu'erh tea is also considered the fine wine of tea and is fermented)
If someone is telling you it is caffeine free, they're lying. White teas are still made from camellia sinensis plant which contains caffeine. Some herbals even have caffeine because there are other herbs out there that have that.
Decaf tea can also contain trace amounts of caffeine. The word decaf means the processing of the herb has been done to remove as much caffeine as possible. However, it may not all be eliminated.
A breakdown by category of caffeine per cup (source: study done by Spoon University website):
White Tea 30-55 mg
Green Tea 35-70 mg
Oolong Tea 50-75 mg
Black Tea 60-90 mg
Coffee 150-200 mg
The lesson to be had here is: the longer and hotter you steep the camellia sinensis plant, the more caffeine you will get per cup, but it also depends on how your tea was processed. You will also get more tannins per cup (that which gives tea the sort of 'bitter' taste when oversteeped).
If you are needing to be caffeine free for health reasons, please refrain from white tea.