Automatically pop up message box

First of all, find which messaging plugin you are using, the default is the standard SRMM Plugin.

SRMM
Open the Options Dialog, and navigate to Events->Messaging.

Under "Automatically pop up window when:", tick the statuses you want the message box to pop up in.

For example, tick 'Online' and 'Free for chat', but disable 'Do not Disturb', so if your status is 'Do not Disturb', the dialog will not popup when you recieve a message but will popup for 'Online' and 'Free for chat'.

TabSRMM 0.9.9.94
Open the Options Dialog, and navigate to 'Message Sessions'->'Message Window'.

Click on the 'Tabs and layout' tab.

In the 'Create Tabs and Containers' section, you will find the various options.

The first option should be ticked ("Automatically pop up the window/tab when a message is received').

The other options specify what happens if the message window is already open, but minimized.

TabSRMM 0.9.9.97
Open the Options Dialog, and navigate to 'Message Sessions'->'Message Window'.

Click on the 'Tabs and layout' tab.

In the 'Messagewindow to appear whenever a contact writes to you - won't select the necessary tab).

'Automatically switch tabs in minimized containers' when a contact in a different tab than the currently selected one writes to you that tab will become the selected one (usually used with 'Popup container if minimized' to show the container window and switch to the relevant tab as well)