The sentence is quite simple and not worth overthinking (and has nothing to do with precedence).
If there is an established correlation between a variable and time (i.e. we know that an increase in time is accompanied by an increase in the variable, and this is a given), then we know the "causal" direction: i.e. time increasing, causes the variable to increase.
Because the alternative hypothesis of "nah-uh, it could be that time only increased because the variable increased first" simply cannot stand given the way time works.
This might sound like a silly observation, but it has important implications for study design trying to prove a causal direction. An important example in medicine is the difference between doing a cross-sectional and a cohort study.
E.g., a cross-sectional study trying to find a link between smoking and cancer might take a group of people, divide it into smokers vs non-smokers, and see how many in each group have cancer vs no-cancer. However, this is weak evidence because a correlation between smoking and cancer could also be interpreted as "people who have cancer are more likely to enjoy taking up smoking".
However, if you perform a cohort study, i.e. take a group of smokers and a group of non-smokers, and follow them up through time, and measure the variable "cancer in smokers minus cancer in non-smokers", and establish a positive correlation of this variable with time, (under reasonable assumptions, such that smoking amount once started is constant and independent of time etc) then you know that "time" is the cause of the cancer difference, since you cannot claim that increased rates of cancer caused time to pass more in the smoking group. Therefore you can claim a causation between time passing and a positive cancer difference related to higher rates in the smoker group. (or, more simply stated, time spent belonging to the smoking group causes a proportional increase in cancer risk).
Furthermore, the weakness of the cross-sectional study, i.e. the possibility that "people with cancer are more likely to take up smoking" has now gone out the window, since smoking as a variable has been taken out of the "time vs cancer" equation (here assumed to be constant and therefore unaffected by time). In other words, by formulating the study in this way, we have examined a very specific causal direction. If we wanted to examine the extent to which the reverse causal direction applies (i.e. how likely it is that people who will eventually get cancer are to take up smoking as time goes by), then we would necessarily have to design a cohort study split into "future cancer vs no-future cancer" and measure the uptake of smoking over time.
Update responding to comments:
Note that this is a discussion over a causal direction rather than one of finding a direct causal link. The question of confounding is a separate one. (i.e. there is nothing to suggest that there isn't an independent third variable that both makes you more likely to be a smoker and increases your chances of cancer with time). I.e., in terms of counterfactual causality, we have not definitively shown that "had it not been for smoking these people would not have gotten cancer". But we have shown that "the association between smoking group and cancer would not have increased had time not passed". (i.e. the association is not down to a snapshot of cancer sufferers mere preference for being in the smoking group or not, but is stengthened over time).