Electric Tester light up on secondary side of Ground
First, 250 µA AC is (just) perceptible to touch, though not as a shock, but usually perceived as a vibration or tingle. It is also enough to light a neon lamp, if that is the tester you used.

That said, you may be getting additional leakage from capacitance from the AC mains to the board, or from surface leakage on a PCB at high humidity. It could also be that you were not at ground, if you're on an insulated surface and are standing near high-tension lines. To check for dangerous leakage, use a tester that actually measures AC current to ground, rather than a test light.

If there is just  250 µA leakage or less, but it is still considered objectionable, the power supply output could be bypassed to ground through a small capacitor, if that does not cause an issue with the following circuitry, which might need to float.

BTW, the laptop I'm using had the same issue: there was a noticeable "buzzing" feel on touching the case until I added a bypass capacitor to ground -- yet the external power supply had a number of safety approvals.