In Franco's historiography, he has been identified as one of the top Republican leaders who was responsible for the murder of the right-wing politician José Calvo Sotelo, an accusation that Burillo always rejected.
In July 1936, he was commander of the 2nd Assault Group based at the Pontejos barracks, attached to the Ministry of the Interior building – in the middle of Puerta del Sol in Madrid.
On 12 July, he was on duty at the Pontejos barracks when he was surprised by the murder of Lieutenant José del Castillo, an Assault Guard officer who had been killed by Falangist gunmen.
The fact that he is the superior of Lieutenant Castillo and both belong to the same Assault group will leave him touched by suspicions about his participation in or knowledge of the murder of the deputy of the "National Bloc".
Once Toledo fell into revolted hands, Burillo was present in different actions of the Front of the center, trying to put order among the militiamen in his column who were demoralized.
Thus, under Burillo's orders, on June 16 the POUM headquarters at the Hotel Falcón was closed and the party's members, including its top leader —Andrés Nin— were arrested on charges of Francoist espionage.
However, in the summer of 1938, the Army of the South under the command of General Queipo de Llano reactivated the Extremadura front with several offensives that caused the consecutive collapse of the Republican lines.
Charged by Franco's courts, he was accused, among other crimes, of being one of those directly responsible for the murder of Calvo Sotelo, something that he would deny from his trial until the day of his death.