Travel eSIMs work by roaming onto local networks. That is the whole mechanism. If data roaming is off for the SAIMING line, the phone will register but refuse to pass data.
It will not cost you anything
The roaming charges people rightly fear come from your home carrier’s own SIM. Turning on roaming for the SAIMING line only affects that line. Your home SIM keeps whatever settings you gave it.
Where the switch is
- iPhone: Settings → Cellular → tap the SAIMING line → Data Roaming.
- Android: Settings → Network & internet → SIMs → tap the SAIMING line → Roaming.
Belt and braces
If you want to be certain your home SIM cannot be billed, turn its own data roaming off, or turn the line off entirely, and leave only the SAIMING line carrying data.