Unfortunately the rep was correct: be the only way to truly prevent data leakage is to remove your SIM card.

I would suggest that when you travel again, get a local SIM and forward your Koodo number to a VoIP service.

Alternatively, you can call your voicemail on occasion with your local line and see if anyone left you any messages.

@Ashish Bhatt - Data leakage typically occurs when your phone “checks-in” with the network to see if it’s still roaming. The best way to avoid data leakage would be to make sure Data AND Data Roaming are turned off. 

Keeping Data ON and Data Roaming off is basically like telling your phone “I would like to use data but only when I’m back in Canada”. The only way for your phone to know where it’s located is to check-in with the network (this typically happens when the phone is restarted). Phone’s are so fast these these days that in that split second many phone applications have a chance to ping the network causing very minimal amounts of data resulting in Easy Roam being triggered, 

Take a look at this page to learn about how you are charged while roaming along with some tips on how to avoid being charged. 

I’ve also heard that a phone with VoLTE enabled will cause a phone to incur micro-usage of data even with data disabled.

Workaround would be to disable VoLTE, but this is problematic for two reasons - iPhones with latest updates no longer offer the ability to disable VoLTE while connected to an LTE network, and the fact that 3G networks are set to be decommissioned in the USA this year...

@Nezgar - That’s actually a good question. I’ll reach out to the team and respond back here when I get an answer.

Best answer by Chris Koodo

@Ashish Bhatt - Data leakage typically occurs when your phone “checks-in” with the network to see if it’s still roaming. The best way to avoid data leakage would be to make sure Data AND Data Roaming are turned off. 

Keeping Data ON and Data Roaming off is basically like telling your phone “I would like to use data but only when I’m back in Canada”. The only way for your phone to know where it’s located is to check-in with the network (this typically happens when the phone is restarted). Phone’s are so fast these these days that in that split second many phone applications have a chance to ping the network causing very minimal amounts of data resulting in Easy Roam being triggered, 

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The FAQ can be somewhat misleading - the instructions might be Ok for Android, but definitely not for iPhone users.
What I have learned recently, is that, besides turning off data roaming , there’s a setting in iPhones: “wifi assist” that must be turned off - and also make sure you have turned off iCloud Drive! 
There’s still no guarantee Easy Roam won’t try to ping to a tower if you turn your device off & on, or come out of airplane mode.  
An issue for us was resetting our devices to the correct time zone! Our iPhones didn’t set to the current time zone automatically, so we had to turn our phones off & back on. That simple maneuver was enough to trigger Easy Roam - even though we had data roaming turned off!   
I think the only thing to do when travelling is to make sure you don’t have Easy Roam as an add-on, possibly suspend your service with Koodo and instead get a phone and / or sim card in the country where you visit.  You cannot depend on Koodo to correct roaming charges that were charged in error since the process with customer service to get things resolved is so difficult. To avoid ‘data shock’ for roaming charges you didn’t incur may be to just not use Koodo when out of country, and resume service when you return.