Serious danger? Your privacy is pretty much nonexistent when you closed-source wallet, since you're connected to their server and it's likely they log everything (where there's no way to prove it's true or false).
But Coinomi does allow you to change the server it talks to (on the mobile version). Don't trust them for privacy, use your own server.
You can actually install a sniffer on your Wi-Fi and see that yes, once you change it it never talks back to them. On mine it has not pinged back for months except for update checks.
--snip--
-Dave
TBH i completely forget about it, but AFAIK by default you're connected to their server and there are very few people who bother change it (since usually people who bother do this would use open-source wallet instead)