A response from 
regarding location-based security:
The last known location of your phone is just one of the signals that we use to detect fraud so please don’t worry about us blocking your card if you don’t have data access. In the absence of data access we can also be a little bit more intelligent about how we use your phone’s last known location. Obviously, if we can tell that your phone was last seen in London 2 minutes ago and we see your card is being used in a bar in Ibiza then there’s a high probability that something is awry. Conversely if we last saw your phone 10 hours ago near Heathrow airport and now we see a transaction in Ibiza then perhaps you’re on holiday. That’s just a simple example but hopefully it illustrates the point.
If you leave your phone at home with it switched off (so its not acquiring a location or sending data) it sounds like the Monzo fraud system is intelligent enough to figure this out.
You can also turn off ‘location-based security’ in the app, via settings just to be safe. Perhaps this setting is designed for users like yourself who aren’t always carrying their phone with them.
Theres certainly a lot of confusion around the location-based security system and exactly how its implemented, so as others have suggested its probably best to speak to customer support 