Reactive value does not update when input is first generated - r

Question

I'm currently trying to develop a large application using modules. One of those module is used to filter a dataset where the user can first select the columns he wants to filter. Once he selects the columns, the user can then select the values for each column.
As it is a two steps process, the option to select the values is not available while no columns have been chosen.
Now, my issue is that when the selectInput used to select values is first generated its value on the server side does not seem to update to the default selection.
Here's an example of what I'm trying to do:
Module UI
filter_ui <- function(id){
ns <- NS(id)
tagList(
uiOutput(outputId = ns("filter")),
uiOutput(outputId = ns("value"))
)
}
Module Server
filter_server <- function(id){
moduleServer( id, function(input, output, session){
ns <- session$ns
mod_values <- reactiveValues()
output$filter <- renderUI({
selectInput(inputId = ns("filter"),
label = "Filter",
multiple = TRUE,
selected = NULL,
choices = list("variable_a",
"variable_b",
"variable_c"))
})
observeEvent(input$filter, {
output$value <- renderUI({
lapply(input$filter, function(i){
selectInput(inputId = ns(i),
label = paste0("Select ",i),
multiple = FALSE,
choices = list("1",
"2",
"3"))
})
})
mod_values$filter <- input$filter
for (j in input$filter) {
mod_values$values[[paste0(j)]] <- input[[paste0(j)]]
}
})
return(mod_values)
})
}
The reason why I'm using uiOutput instead of just a regular selectInput in the UI is because in the application there are other arguments that will influence what is rendered.
App
ui <- function() {
fluidPage(
filter_ui("filter")
)
}
server <- function(input, output, session) {
filter_value <- filter_server("filter")
variable <- reactive({filter_value$filter})
value <- reactive({filter_value$values})
observeEvent(variable(), {
print(value())
print(variable())
req(value())
n <- 0
for (i in variable()) {
n <- n + 1
print(paste0("the ", n, "th loop value is ", value()[[i]]))
}
})
}
shinyApp(ui, server)
Now, the first time I select any filter the value does not update and I get for example:
[1] "variable_a" "variable_c"
[1] "the 1th loop value is 1"
[1] "the 2th loop value is "
While I need:
[1] "variable_a" "variable_c"
[1] "the 1th loop value is 1"
[1] "the 2th loop value is 1"
I guess my issue comes from a wrong use of reactivity but I can't seem to find what. Any help would be greatly appreciated!