Changing the transformation of the y-ticklabels back to the original y-axis transform would give you the desired ticks on the left side of the axes.
plt.setp(ax.get_yticklabels(), transform=ax.get_yaxis_transform())
Complete code for reproducibility
import matplotlib.pyplot as plt
X = range(-10,5)
y = [i**2 for i in X]
fig, ax = plt.subplots(1,1, figsize=(10,8))
plt.plot(X, y)
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.spines['left'].set_position('zero')
plt.setp(ax.get_yticklabels(), transform=ax.get_yaxis_transform())
plt.show()
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