MySQL Trigger: Insert depending on NEW.column of type enum
I had to use delimiter to make it work but because delimiter is a mysql-console command it didn't work by putting it in my script.

phpMyAdmin has a different way to set a delimiter. Below of the script-input there is another input to set a delimiter so at then and my script looked like this:

CREATE TRIGGER insert_after_new_kpi_trig
    AFTER INSERT ON KPI
    FOR EACH ROW
    BEGIN
    IF NEW.kpi_type = 3 THEN BEGIN
        INSERT INTO ProjectKPIData (project_id, kpi_id, value) SELECT p.id, NEW.id, 0 FROM Projects p;
        INSERT INTO TeamKPIData (team_id, kpi_id, value) SELECT t.id, NEW.id, 0 FROM Teams t;
        END;
    ELSEIF NEW.kpi_type = 1 THEN
        INSERT INTO TeamKPIData (team_id, kpi_id, value) SELECT t.id, NEW.id, 0 FROM Teams t;
    ELSEIF NEW.kpi_type = 2 THEN
        INSERT INTO ProjectKPIData (project_id, kpi_id, value) SELECT p.id, NEW.id, 0 FROM Projectsp;
    END IF;
    END $$ --Thats the delimiter I set.