I agree that there are few that "build this service in" to their devices. I couldn't find inverters with phone control with a quick search, so you'll need to do a deep research effort to try and find models like Victron that might have this.
There are numerous DIY ways to achieve this, but we don't know your skill level. If you make sure that the inverter you get is already "remote-control" enabled, then it will have a remote switch (usually w/ a "phone" rj-12 type of cable), and a plug for it, and/or a wireless remote fob kind of switch.
Any of these are acceptable, as now all you have to do is look for a wireless or phone-controlled relay that is reasonably easy to wire into this remote control circuit of the inverter. If you are a little bit handy, there are many youtube vids for wiring a remote fob control into any inverter, such as this vid:
youtube.com/watch?v=XoeU5iJnbwY
Short distance control = a relay w/ bluetooth support. Long distance control = a relay with Internet or cellular services support. For either of these, just wire the relay into your inverter's remote control circuit, and then control it remotely w/ your phone.
Hope this helps ...