When you are in Singapore, there is nothing to do, by default data roaming is disabled on your phone.
When you go overseas, there is nothing to do as well if you’re not using data overseas. By default Zero1 supports pay as your roam (when you are overseas) for outgoing SMS, incoming calls, outgoing calls. Incoming SMS is free (so you can receive all your SMS OTP).
There is no Pay As You Roam for data. If you try and use data overseas (even if data roaming is turned on on your phone) you cannot do it unless you subscribe to their International Roaming Data Packs. Hence, you won’t be charged anything for data for any accidental usage since no data will load.
Pay As You Roam service (for calls and SMS but not data) is provided free of charge. If you don’t anyhow answer calls, make calls, or send SMS when you are overseas you won’t be charged anything.
Now if you want to use (Zero1) data when you are overseas, you need to subscribe their International Roaming Data Packs. Then enable data roaming on your phone. There is no roaming pack for calls and SMS, it charges based on the Pay As You Roam rates.
I suggest you read the Zero1 FAQ page especially on the following sections.
https://support.zero1.sg/kb/c30/roaming-call-and-sms.aspxhttps://support.zero1.sg/kb/c32/roaming-data-plans.aspx
To me personally I think Zero1 is already almost a full fledged telco as it supports Pay As You Roam and this service is provided for free, which some MVNOs (like GOMO) don’t even have. This is important when you need to make an emergency call (for emergency services) or receive calls when you are overseas, you can do it.
Also I don’t subscribe to their International Roaming Data Packs when I want to use data when I’m overseas as the Zero1 rates are not really cheap. Instead I will just buy an eSIM overseas data plan from online (Qoo10/Shopee/Lazada) and activate it just before leaving Singapore.