Stalin's policy was to create a problem, then present himself as the hero for fixing it, in order to consolidate his power.

For example, Stalin pushed for intensive Collectivization/Grain seizures in the Early 30s, for the sake of his five year economic plan. The Party followed his orders and aggressively seized all they could. Stalin then issued a statement, "Dizzy with Success", wherein he called out Party officials for being too zealous (hence 'Dizzy with success'), and had them reined in. Since he issued such a statement, the people were able to direct their anger at Party Officials (who could then be 'punished' and removed to make room for someone more loyal), with Stalin's image being left intact, despite it being his quotas being followed.

The same was true for the Great Terror. Stalin definitely caused it. He ordered Ezhov and the rest of the NKVD to extract confessions via torture, with the intention that the "confessions" would implicate others, and so on, leading to more and more arrests. It began in late 1934, with the assassination of Leningrad Party chief Sergei Kirov by Leonid Nikolaev. Nikolaev was acting on his own because he believed His wife was cheating on him with Kirov, but Stalin - known for being paranoid and Controlling - wanted to believe that his enemies were behind Kirov's assassination, so he used it as a pretext to have his old rivals Kamenev, Zinoviev and Bukharin tried for treason, and then used their former high ranks to claim that they were part of a vast "conspiracy" to destroy the Soviet Union. This was the pretext for the Terror.

As for Ezhov, he was completely under Stalin's thumb. The Secret to Stalin's power was his absolute control over the Secret Police, and making sure that his followers were either completely devoted or terrified of him. Ezhov was no exception. For example, between 1937 to 1938, Ezhov was the second most frequent visitor to Stalin, after Prime Minister Molotov (Kotkin, 2017). All of his actions and decisions went through Stalin first before being implemented. That being said, there is some truth to the idea that Ezhov was partially acting on his own will. Stalin wanted "enemies" that he could destroy at a whim, which he could also use to remind his followers that he was number 1, so Ezhov and another Man, Evdokimov, manufactured them in order to satisfy Stalin's desires. This can be summed up as "Stalin's followers telling their boss what he wanted to hear".

The Purge ended when Stalin was satisfied and saw that he could boost his popularity again, similar to the "Dizzy With success" example mentioned previously. In 1938 the Purges were winding down, but Stalin gradually began to undermine Ezhov and Evdokimov's positions in the NKVD. Evdokimov was undermined when a new man, Genrik Lyushkov was assigned to him. During the Purge, Most of the NKVD were made up of close associates of Evdokimov and Ezhov, so it was a huge blow to Evdokimov when he found out that an "outsider" was assigned to him and refused to follow his orders. Yezhov had Lyushkov reassigned to the far East, but suffered a huge blow to his image when Lyushkov then defected to the Japanese. Finally, in November 1938, Stalin assigned his fellow Georgian and close associate Lavrenty Beria, to replace Evdokimov and Ezhov's loyalist Frinovsky as the first deputy and head of the UGB/Counterintelligence division. After this, Evdokimov, Ezhov, Frinovsky and their associates would be arrested and replaced with Beria's team, who were also more loyal to Stalin. As before, Stalin would use them as "scapegoats" like the collectors in the early 30s, and take credit for "fixing" the Policy he himself started.

Summary

Yes, Stalin started the purges. He initiated them due to fear of imagined enemies and a desire to put his Closest associates, who were not spared, under his thumb and make room for new, up and coming followers to replace the old. Ezhov and Evdokimov acted on his behalf out of a desire to please him, and far from being "horrified and angry", he cynically and gradually undermined Ezhov and Evdokimov to remind them who was boss, and give his new NKVD boss Beria a chance to prove himself. Like most cases, Stalin created the problem and took credit for fixing it.

References Stalin, waiting for Hitler, 1929-1941 by Stephen Kotkin

Agency and Terror: Evdokimov and mass killing in Stalin's great terror, by Stephen Wheatcroft.