While there is no event fired upon adding a module to a page, you can simply retrieve one (or all) of your ModuleSettings or TabModuleSettings in the Page_Load handler. If the retrieved setting is null, then the module is being added to the page the first time, in which case you can then initialize one (or all) of the settings.

If my module has more than a few settings that are accessed repeatedly, I usually create a configuration class which handles the loading/saving of all settings and their first time initialization when the module is added to the page. As an alternative, rather than initializing the settings when the module is first added to the page, you can simply return the appropriate default value when retrieval of a setting returns null.

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Bill, WESNet Designs
Team Lead - DotNetNuke Gallery Module Project (Not Actively Being Developed)
Extensions Forge Projects . . .
Current: UserExport, ContentDeJour, ePrayer, DNN NewsTicker, By Invitation
Coming Soon: FRBO-For Rent By Owner