A quantum object is its own thing - it has both wavelike and particle-like properties.
Measurement here might be better understood to "filter out" any parts of the wave that don't agree with the measurement. So a precise measurement will project out a lot of the wave, giving you something more localized and particle-like. A fuzzy measurement will project out only a bit of the wave, giving you something that's still spread out and quantum and wave-like.
The article says "The fuzzier atom rustles more easily and records the path of the photon. In tuning up an atom’s fuzziness, researchers can increase the probability that a photon will exhibit particle-like behavior".
I think we're just seeing decoherence in action here. If the photon interacts with the atom, it becomes entangled with the environment (the atom). Giving the atom a higher temperature results in it having a higher probability of it interacting with the photon, and decohering.
And I think the individual photon doesn't have a mixture of a certain % of wave or particle like nature. It's just that there is a certain probability that it will decohere (interact with the atom), so if you turn up the temperature of the atoms, you'll just see a greater % of the photons decohering when they interact with those atoms.
That's just my amateur understanding of the situation, so I'm happy to be corrected by someone who knows better. Also, I don't have access to the paper itself (https://journals.aps.org/prl/abstract/10.1103/zwhd-1k2t) as it's paywalled and not on scihub.
Quantum mechanics is fascinating!