Siri-initiated HomePod audio shows on my iphone

My daughter uses a HomePod mini for white noise at night, which she triggers each night with “hey siri, play white noise.” It then usually shows on my iPhone as though I started it from my phone and airplay’d it to the homepod (ie., shows as media playing on my Lock Screen).

this causes two problems:

1) I have to be careful not to accidentally pause the white noise from my iPhone, as it’ll wake her;

2) if I play a podcast/music on my iPhone, it defaults to her homepod and startles her.

how do I prevent her homepod audio from showing as a default on my Lock Screen and as the pre-selected airplay speaker when I start a podcast/music after she goes to bed?

many thanks!