AddTime() is not the cause of your anomaly. Your query mistake is.
In a Group By query, non-aggregated columns omitted from the Group By clause return arbitrary values when the column does not maintain a strictly 1:1 relationship with Group By columns. When we add in the required Group By columns, your anomaly goes away:
SELECT
a.codasig_cita, a.hora_cita, pe.duracion,
SEC_TO_TIME(SUM(TIME_TO_SEC(pe.duracion))) AS duracion2,
ADDTIME(a.hora_cita, pe.duracion) AS "add_correct",
ADDTIME(a.hora_cita, SEC_TO_TIME(SUM(TIME_TO_SEC(pe.duracion))) ) AS "add_wrong"
FROM asig_cita2 a, citas_proc_empl2 cpe, proc_empl2 pe
WHERE cpe.codproc_empl=pe.codproc_empl AND a.codasig_cita=cpe.codasig_cita
GROUP BY a.codasig_cita;
+--------------+-----------+----------+-----------+-------------+-----------+
| codasig_cita | hora_cita | duracion | duracion2 | add_correct | add_wrong |
+--------------+-----------+----------+-----------+-------------+-----------+
| 741550 | 07:00:00 | 00:00:00 | 00:00:00 | 07:00:00 | 07:30:00 |
| 742135 | 07:30:00 | 00:15:00 | 00:15:00 | 07:45:00 | 08:15:00 |
| 742413 | 08:00:00 | 00:15:00 | 00:15:00 | 08:15:00 | 08:00:00 |
| 742460 | 07:45:00 | 00:15:00 | 00:15:00 | 08:00:00 | 08:00:00 |
+--------------+-----------+----------+-----------+-------------+-----------+
SELECT
a.codasig_cita, a.hora_cita, pe.duracion,
SEC_TO_TIME(SUM(TIME_TO_SEC(pe.duracion))) AS duracion2,
ADDTIME(a.hora_cita, pe.duracion) AS "add_correct",
ADDTIME(a.hora_cita, SEC_TO_TIME(SUM(TIME_TO_SEC(pe.duracion))) ) AS "add_wrong"
FROM asig_cita2 a, citas_proc_empl2 cpe, proc_empl2 pe
WHERE cpe.codproc_empl=pe.codproc_empl AND a.codasig_cita=cpe.codasig_cita
GROUP BY a.codasig_cita, a.hora_cita, pe.duracion, add_correct;
+--------------+-----------+----------+-----------+-------------+-----------+
| codasig_cita | hora_cita | duracion | duracion2 | add_correct | add_wrong |
+--------------+-----------+----------+-----------+-------------+-----------+
| 741550 | 07:00:00 | 00:00:00 | 00:00:00 | 07:00:00 | 07:00:00 |
| 742135 | 07:30:00 | 00:15:00 | 00:15:00 | 07:45:00 | 07:45:00 |
| 742413 | 08:00:00 | 00:15:00 | 00:15:00 | 08:15:00 | 08:15:00 |
| 742460 | 07:45:00 | 00:15:00 | 00:15:00 | 08:00:00 | 08:00:00 |
+--------------+-----------+----------+-----------+-------------+-----------+