ACUTE effects of drinking distilled water
The idea behind the myth that distilled water is harmful is that its low osmolality ("tonicity") could dangerously decrease the blood osmolality, which is normally: 285-295 mmol/kg. But distilled water has only slightly lower osmolality (0 mmol/kg) than tap water (~3 mmol/kg) (SGSM.ch, Table 2), so if drinking appropriate amounts of tap water does not significantly lower blood osmolality, distilled water also shouldn't.
The difference between tap and 100% pure water is so slight that it'll never cause hyponatremia. What WILL cause hyponatremia is drinking way, WAY too much water in a short span of time. That'll dilute your blood (hyponatremia) from ions that you need as your kidneys desperately try to get rid of all the water. This is entirely mitigated by eating foods around the same time that are not entirely deficient in minerals like salt (pretty much all foods).