The other answers give good arguments to show that God did not directly cause the events in the prophecy. The OP’s question, however, leads me to also consider whether or not God played an indirect role in those events.
Looking at the text of Hosea as a whole, the book is replete with dire threats and warnings against Israel. However, the only violent action that is directly attributable to God is confined to the words of the message/prophecy itself.
Therefore I have cut them in pieces by the prophets; I have slain them
by the words of My mouth; And the judgments on you are like the light
that shines. –Hosea 6:5
The shocking language of Hosea was therefore intentional, meant to lay bare the sins and wickedness of Israel, and to alert it to the danger that lay ahead. And though God was unquestionably angry, he did not gloat over their impending doom.
How can I make you like Admah? How can I treat you like Zeboiim? My
heart is turned over within Me, All My compassions are kindled. –Hosea
Quite the contrary, the thought of what was going to happen stirred God’s compassion and moved him to act, that is, to send warning by means of the prophecy. Like the prophecies before it, it was a gesture of God’s goodness and mercy.
But I have been the Lord your God since the land of Egypt; I will make
you live in tents again, As in the days of the appointed festival. I
have also spoken to the prophets, And I provided many visions, And
through the prophets I spoke in parables. –Hosea 12:9-10
Furthermore, woven into the prediction of doom and destruction was a call to repentance and a message of hope that there was still time to turn to God and be saved.
“Come, let’s return to the Lord. For He has torn us, but He will heal
us; He has wounded us, but He will bandage us. –Hosea 6:1
So as for you, return to your God, Maintain kindness and justice, And
wait for your God continually. –Hosea 12:6
If Israel heeded God’s words, he would relent of his anger. But it did not. What role then did God play in the fulfillment of the prophecy? In my understanding of the text, the prophecy was not fulfilled by any direct or indirect action of God. If God can be said to be responsible at all, it is only by the withdrawal of his presence and help.
Whereas before he had been there to aid them.
But they did not know that I healed them. I pulled them along with
cords of a man, with ropes of love, And I became to them as one who
lifts the yoke from their jaws; And I bent down and fed them. –Hosea
For there is no savior besides Me. I cared for you in the
wilderness, In the land of drought. –Hosea 13:5
Now he would go away and withdraw his help.
I will go away and return to My place Until they acknowledge their
guilt and seek My face; –Hosea 5:15
They will go with their flocks and herds To seek the Lord, but they
will not find Him; He has withdrawn from them. –Hosea 13:5
But Israel chose to face its enemies alone. In the final analysis Israel and no one else was responsible for its own destruction.
It is to your own destruction, Israel, That you are against Me,
against your help. –Hosea 13:9
For God is “the Holy One who is faithful” (Hos 11:12). Unlike men, God does not return evil for evil.
I will not carry out My fierce anger; I will not destroy Ephraim
again. For I am God and not a man, the Holy One in your midst, And I
will not come in wrath. –Hosea 11:9
If we think God capable of evil, then we would be guilty, just as the Israelites were, of having no understanding of God (Hos 4:11, Hos 5:4).
For I desired mercy, and not sacrifice; and the knowledge of God more
than burnt offerings. –Hosea 6:6 KJV