The simplest answer to this sort of question is to slightly modify your design so that there is a Button downstream from the TimeRangePicker and upstream from the Search.
You would give that Button module an allowAutoSubmit param of False. (Whether you also give it an allowSoftSubmit param of False is a separate matter and entirely up to you.)
What this will do, is that the initial autoRun push kicks off that search, the search results populate the Tabs, but then when it hits the indomitable Button with allowAutoSubmit set to False, the push is stopped. The user than has to click the green button in order to proceed.
If you take your question and you replace TimeRangePicker with Pulldown, there is another answer involving the Gate module. Gate is an invisible module that has 2 different "gatelike" use cases. The first is that it can block pushes until one or more keys are set from upstream modules So you can have it block as long as a "select..." item is selected in one or more Pulldowns. Here however, the TimeRangePicker doesn't really have a "select..." state so it always has a key so Gate would have nothing to grab onto.
