Hamachi shows A.Ok. Ping to each other is success. But can't make a link in application.

Hello,

I have installed Hamachi for few months and was a happy user, until I got my corded network installed in my house.
 
Here is the working network topology:
[ ISP ] <=(4G Network)=> [ Mobile Phone ] <=(USB Tethering)=> [ My Host Computer ]
Diagnosis shows A.OK. Ping to each other succeed. Application in different computers sees each other.

The problem network topology:
[ ISP ] <=(Fiber)=> [ Fiber Modem ] <=(PPPoE)=> [ Wireless AP ] <=(Wifi)=> [ My Host Computer ]
Diagnosis shows A.OK. Ping to each other succeed. But specific application does not communicate at all.

I have tried many configurations, like turning on DMZ zone in modem and AP, or directly connected to fiber modem, but the situation is still the same: I can ping to each other, but can't see each other in application. Tried to search for similar discussion topics too, but none was seemly similar.

I have to migrate to the second topology since the latency and bandwidth are much better than the mobile one, but I never expect to have such a weird problem that is partial working, from the successful experience of mobile network.

Any thoughts, possible causes, or possible solution are appreciated.