Sametime is expected to have the ability to send PUSH notifications for Mobile Client users, even if users are simultaneously logged in anywhere (Web, rich, standalone clients).
Currently, APNS PUSH notification about new chat messages is not being received for IOS\Mobile users if the user has logged in to Notes Sametime embedded client\connect client(Rich Client).
As per the current design when users are logged in to Web chat, it will send push notifications on new chat to the mobile client.
This is because both the Mobile and Web clients access chat through the Sametime Proxy server.
Whereas Rich clients like Notes embedded Sametime client or the standalone connect client, connect directly to the Sametime Community server.
By design, when rich clients are active, the Sametime Community server does not notify the Proxy server of "new chat" since its web/mobile clients are not the "active" client.
The chat will be seen because of persistent chat, but this is why notifications are not sent to mobile users in this scenario.