HomeKit and Home App substitute question

I have a quick question that I can’t seem to find an answer to.

If I use a more advanced HomeKit app than Apple’s default Home, will the scenes/automations/etc work when my phone, where the app is installed, is not at home?

I have been slowly and surely smartifying my home. Everything is HomeKit and working OK. Now that I have a reasonable number of accessories, I am at the point where I would like to make my smart home, well smarter.

The Home App is quite limited when it comes to automations and scenes. My first desire would be to be able to use some basic logic (i.e. If/Then statements would be cool). Websites and Youtube videos all suggest using alternative Apps rather than Home (e.g. Home+, Eve, etc) but I can’t figure out what happens when I leave the house.

HomeKit hubs (mine has defaulted to a HomePod Mini) don’t get the software, so if I am not at home with my phone does the new automation simply not run? Or despite the logic not being available in Apple’s App, it is supported by the underlying HomeKit environment?