Adding Siemens Whole House SPD to Pseudo neutral Siemens GFCI
Remember when I warned you not to get tempted to use the pseudo-neutral for anything else?   This.  

This is exactly the sort of "scope creep" I'm talking about.  "Oh, I've got another thing that needs neutral, I'll just grab it from there". Nuh-uh. No way. 

See, the GFCI uses neutral only for its  own internal power, it's a tiny load.  The surge suppressor doesn't use neutral for internal power, it uses it to suppress surges on the neutral: it aims to flow hundreds of amps down the neutral. 

That would vaporize the tiny transformer.  

It's also possible the surge suppressor has some lights on it.  Those are probably to indicate faults such as a lost pole or lost neutral. The latter being particularly dangerous in North America, but a big nothingburger in your part of the Philippines. 

(To our readers, the Philippines is in the midst if a transition between North American 120/240V and European 230V.  The first step of the process was deleting center neutral. Those neighborhoods get 2 legs of power, neither one near ground. This is unlike Europe, where one of the legs of power is neutral and thus near ground.)  

The simple fact is, surge suppression in the Philippines is a difficult problem. At first glance, Euro style surge suppressors are a better fit, because they only protect surges on 2 poles.  However, Euro units expect there to be a neutral that is near ground, so they may not br a good application.  

Indigenous units actually built for the Philippines would be the best choice.  Otherwise you have two options, and I would consult with the factory: 


hook the surge suppressor's neutral and ground to your earthing system. 
if the suppressor can stand 240V across hot-neutral, wire both hots to one leg of power and neutral to the other leg of power. But I would not do that without factory consultation.  


Keep in mind, you are seeing the spec call out a higher voltage across the 240V wires because it should be that way for 240V.  You can't outsmart the factory, they are pretty smart.