Certainly in the UK you can get the 2fa app popup in store if you tap to pay with your phone rather than a card. It’s analogous to going for a contactless payment with a card and them asking to insert the card and type the pin (which sometimes happens). It’s pretty rare (as in I have done the vast majority[1] of my payments using contactless on a phone for a couple of years now and I think it’s happened once to me).

[1] Like probably 99%+. I scarcely ever have a card on me and never use cash.

I'm pretty sure that's what your parent is describing.

In my case, I often spend multiple days at my parents' house. Now, I mostly don't order online, but sometimes something comes up and in that kind of situation, most merchants will have me go through the verification.

Since this doesn't happen frequently, I'm more likely than not to not have hauled my secondary phone, especially since I very much prefer traveling light. Now, could most of those occasional purchases not have waited for my return home? Eh... most probably could've. Doesn't make it less annoying, though, for no good reason.