What care and precautions do I need to take for the cylindrical vision?

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Keep regular follow ups with your optometrist and eye doctor for repeated refraction for every 3 to 6 months. His refraction will keep on changing till 20 to 25 years of age as the eye grows and the shape of the cornea keeps changing. The main thing is avoiding amblyopia (lazy eye). If he keeps seeing blurry images, then his vision would not develop properly. So, for good vision development he must see clearly, which would be possible with best refraction. If refraction changes rapidly, then there could be another thing to look for, such as keratoconus, but that is in adults usually at the age of 20s. For now, just get regular checkup and keep using glasses or contact lens as prescribed by his doctor. Everything will be fine.