The Guinnes book of records is more a marketing tool than a scientific source. People pays money for proposing something, one or a few judges from the organisation travel to your place for one or two days and if nobody says otherwise, put you in the book. The amount of scientific work and effort done by them to refute this proposal is close to zero.
C4 Photosynthesis evolved from C3 several times. Is typical of Poaceae, (grasses, cereal, bamboo), and also appear in a few plants of other families adapted to dry and desertic areas. There is a recent review of C4 plants (Sage 2016, Journal of Experimental Botany 68) that list each known genus with this kind of photosynthesis. In 2016 the huge genus Euphorbia was the only known genus with a few trees using C4 photosynthesis. Bamboo are not trees but its ecological role is similar in any case
Paulownia does not appear in this list. In fact there is not any plant in the list from the order Lamiales
I didn't find a recent scientific source claiming that is a true C4 plant. Maybe C4 is facultative/not the common way of photosynthesis for this tree, a mix between C3 and C4? Maybe has been modified genetically
Or perhaps this is just a myth.
If is not a true C4 plant, could run in standard mode C3 when provided with water and manure, and will move to the economic mode C4 in dry areas, thus the increase of oxigen produced is debatable.
Crassulacean Acid Metabolism (CAM) on the other hand is present in a few Lamiales but not in Paulowniaceae. Is typical of succulents in family Crassulaceae.