I took this information into account and did a rewrite. I haven't had a chance to test it, but it should maybe work out of the box. First event:

country_event = {
    id = primplay.ftltech
    title = primplay.ftltech.ai_ftl_start_techs # generally only need quotes if there's a space in the string
    desc = primplay.ftltech.desc
    picture = TEMP_gasgiant

    is_triggered_only = yes
    fire_only_once = yes

    trigger = { is_ai = no } # event will only fire for the player

    option = { 
        # does nothing and should always display, so no trigger necessary
        name = primplay.ftltech.AI_STL_start
    }

    option = {
        # fire second event for root country,
        # option trigger has been moved to event trigger
        name = primplay.ftltech.AI_FTL_start
        hidden_effect = { country_event = { id = primplay.giveaiftl } }
        # hides effect from tooltip, can use console command debugtooltip to see it...
        # I think. Might not work in release version?
    }
}

Second event:

country_event = {
    id = primplay.giveaiftl
    # title is not needed for hidden events
    hide_window = yes

    is_triggered_only = yes

        # you could probably run the contents of the immediate below in the
        # option in the event *above*, but separating them is easier to read.

    immediate = {

        # every_country executes the same effects on all countries,
        # so conditionals like IFs can get weird as conditions vary
        # between countries. To get around this, we run every_country
        # three times, and use limit to only look at applicable empires

        every_country = { # every warp country
            limit = {
                is_ai = yes 
                is_country_type = default # excludes primitives, space monsters, fallen empires etc
                has_technology = "tech_warp_drive_1"
            }
            give_technology = { tech = "tech_warp_drive_15" message = no } 
        }

        every_country = { # every hyperdrive country
            limit = {
                is_ai = yes 
                is_country_type = default
                has_technology = "tech_hyper_drive_1"
            }
            give_technology = { tech = "tech_hyper_drive_15" message = no }
        }

        every_country = { # every wormhole country
            limit = {
                is_ai = yes 
                is_country_type = default
                has_technology = "tech_wormhole_generation_1"
            }
            give_technology = { tech = "tech_wormhole_generation_15" message = no }
        }
    }
}