The solution here is a filter plugin. Plugins are always run after the filter they augment and are handed the instance that is created. So, using this, you could, for example, have a plugin for BS.Tooltip that checks for some other property or setting and automatically shows it on startup. I don't have a ton of examples of this in public repositories, but here's one from Bootstrap:
https://github.com/anutron/mootools-bootstrap/blob/master/Source/Behaviors/Behavior.BS.FormValidator.js#L39
Your code would define a new plugin and then reference the instance and call .show() if the api has some flag set to true.
Note that the API handed to this plugin is the plugin's, not the filter it augments. I.e. if you have a filter called Foo and you create a filter that augments Foo with Bar, the API handed to your plugin is for Bar (data-bar-options, etc), not Foo. If you want to drop your flag into the Foo options, you'll need to grab those values with a new instance of BehaviorAPI:
Behavior.addGlobalPlugin("Foo", "Bar", {
setup: function(element, apiForBar, instanceOfFoo){
var apiForFoo = new BehaviorAPI(element, 'Foo');
//check for the flag on either api
var autoShow = apiForBar.get('showOnStart') || apiForFoo.get('showOnStart');
if (autoShow) instanceOfFoo.show();
}