It is because he was not as tyrant as we think. He was probably tyrant to the world, but not to his sister. In fact he loved her so much that he became the chariot driver himself for Devaki and Vasudeva and set off to transport the newly wedded couple to their home:
Kaṁsa, the son of King Ugrasena, in order to please his sister Devakī
on the occasion of her marriage, took charge of the reins of the
horses and became the chariot driver. He was surrounded by hundreds of
golden chariots. [SB - 10.1.30]
But on the way he heard the omen and got desperate. He got so desperate that he couldn't see what's right and wrong and proceeded to kill Devaki directly:
Kaṁsa was a condemned personality in the Bhoja dynasty because he was
envious and sinful. Therefore, upon hearing this omen from the sky, he
caught hold of his sister’s hair with his left hand and took up his
sword with his right hand to sever her head from her body. [SB -
10.1.35 ]
Killing Devaki right on the spot was undoubtedly a far better solution than imprisoning her with Vasudeva. But he didn't do it as Vasudeva made him realize that Devaki was not the threat, but her children and promised Kamsa to handover his new born children:
Vasudeva said: O best of the sober, you have nothing to fear from your
sister Devakī because of what you have heard from the unseen omen. The
cause of death will be her sons. Therefore I promise that when she
gives birth to the sons from whom your fear has arisen, I shall
deliver them all unto your hands. [SB - 10.1.54]
So Kamsa let them live, not as prisoners but like free prince and princess. And when in due course of time the first child was born, to keep his word, Vasudeva went to hand over the child to Kamsa. But Kamsa was probably not that tyrant, or probably he loved his sister more. So instead of killing the child he was impressed of Vasudeva's truthfulness and said:
O Vasudeva, you may take back your child and go home. I have no fear
of your first child. It is the eighth child of you and Devakī I am
concerned with because that is the child by whom I am destined to be
killed. [SB - 10.1.60]
But later on once Narada visited Kamsa and said how all Yadus are demigods and have been born to kill the demons. This made Kamsa doubtful and he thought any of the eight child could be Vishnu. Only then he decided to imprison them. But because by that time he had already seen the truthfulness of Vasudeva, he knew Vasudeva would certainly hand over all his future children as promised. So the best strategy for him was to have Vasudeva and Devaki give birth to the children and kill them one by one. Once the eighth child was killed he could rest assured. Probably that is why along with his love for his sister, he allowed Vasudeva and Devaki to live together in prision under his supervision.
REFERENCE: Shrimad Bhagavatam, Canto 10, Chapter 1