Calculating months of follow-up with pyears() of survival package - r

Question

I want to calculate the person-time of follow-up by calendar month. In my example, I have three subjects, with different times of follow-up. I want to know if the rates of the event vary by year tertiles, so I want to sum up the time at risk they spend in each of the tertiles.
library(lubridate)
library(survival)
event <- c(1,1,1)
id <- c(1,2,2)
followup_time <- c(365, 365*2, 365*3)
right.date <- c(ymd("2012-06-01"), ymd("2013-09-01"), ymd("2011-01-01"))
left.date <- right.date-followup
tertile <- cut(month(right.date), c(0,4,9,12), include.lowest = T)
df <- data.frame(id, left.date, right.date, followup_time, event, tertile); df
id left.date right.date followup_time event tertile
1 1 2011-06-01 2012-06-01 365 1 (4,9]
2 2 2011-09-01 2013-09-01 730 1 (4,9]
3 2 2008-01-01 2011-01-01 1095 1 [0,4]
sum(df$followup_time)
[1] 2190
Using the package survival in R, function pyears() I get the following results. However, although the number of subjects and events are correct, the person-time of follow-up is incorrect, according to my needs.
s <- Surv(time = followup_time, event = event)
summary(pyears(s ~ tertile , scale = 1))
Call: pyears(formula = s ~ tertile , scale = 1)
number of observations = 3
month N Events Time
-------- --- -------- ------
[0,4] 1 1 1095
(4,9] 2 2 1095
(9,12] 0 0 0
I expect the following results, which correspond to the sum of the time at risk each subject spent in each of the intervals.
month N Events Time
-------- --- -------- ------
[0,4] 1 1 547.5
(4,9] 2 2 547.5
(9,12] 0 0 547.5
Some people use the function tcut() from this same package to do this kind of operation for calculating person-time, but I did not have satisfactory results.

Answer 1

I don't understand the confusion (or maybe it's really simple and nothing to do with survival package functions):
df
#--------
id left.date right.date followup_time event tertile
1 1 2011-06-02 2012-06-01 365 1 (4,9]
2 2 2011-09-02 2013-09-01 730 1 (4,9]
3 2 2008-01-02 2011-01-01 1095 1 [0,4]
month(right.date)
#[1] 6 9 1
It has to do with how the default R cut function works. Intervals are closed on the right. I happen to find that most people expect the intervals to be closed on the left, and if you want that you would execute:
> df <- data.frame(id, left.date, right.date, followup_time, event, tertile); df
id left.date right.date followup_time event tertile
1 1 2011-06-02 2012-06-01 365 1 [4,9)
2 2 2011-09-02 2013-09-01 730 1 [9,12]
3 2 2008-01-02 2011-01-01 1095 1 [0,4)
> s <- with(df, Surv(time = followup_time, event = event))
>
> summary(pyears(s ~ tertile , scale = 1))
Call: pyears(formula = s ~ tertile, scale = 1)
number of observations = 3
tertile N Events Time
--------- --- -------- ------
[0,4) 1 1 1095
[4,9) 1 1 365
[9,12] 1 1 730