Probability of finding a particle outside it's light cone

Question

Say we just created a particle (high probability of one-particle state), is the probability of a very far away detector getting triggered at the time of creation (probability of finding a particle outside of its light cone) zero according to QFT?

Since we can detect particles and make histograms of the positions where they're found using detectors, this seems like a reasonable question to ask. I hope that QFT says that detector cannot detect particles outside its lightcone because if that's not the case, we can imagine an experiment where information can be sent FTL:

Consider a ridiculous amount of hydrogen atoms/electrons near person A and a very far away B measuring the rate of particles he detects. So when A makes some movement, if the probability outside light cone changes immediately, B's rate of detection immediately changes and hence this can be used for communication.

If you say that the probability outside light cone doesn't change immediately, that leads us to a grave situation. Assume A himself has a detector, and if he sweeps/detects most of the particles (sweeps through the high probability region, peaks). It makes zero sense to say B observes a same rate of particle detection since particles are already 'used' up by A.

(Some clarification: When I say particles near A, I mean by this is that we intuitively have an idea that particles/fields must have some kind of probability distribution. It is reasonable to assume that there is some peak in distribution of atoms/electrons of my phone in my hand and probability of electrons of phone's atoms is extremely low far away. So even if QFT doesn't have position operator or whatever, it should somehow be able to talk about this.)