Search API Panels Display and Contexts
It's about time this got a proper answer. Here's that explained as a step-by-step:


Creating a Search API view. None of this will work unless, when you initially create the view, you choose one of the Search API options like "Show [Search Index]" and the appropriate index instead of "Show [Content]" in the drop down at the very start of the views creation process.
Giving it a Context view display. A "Context view" is a type of View Display like a "View block" or a "View page" or an "Attachment view" etc. Create one with the "Add" button at the top of the View edit page.
Load it as a Context in Panels or Page Manager. The thing that is special about Context views, is that systems built on cTools contexts (like Panels and Page Manager) can load the view early on in the process, and also, analyse it so they know what types of data to expect. In the Contexts page for your Page Manager page or Panel, add a context, choose Views, then find the right view.
Place each part of the view as Content. Because cTools is loading the View as a context, and because cTools knows what Views are and how to make sense of them, it knows exactly what elements of the view it's going to get. If it was a views block, all it can do is just dump the whole output of the block somewhere, but since it's taking the time in the Context stage to analyse and make sense of the View, it can figure out that it's going to get seperate rows, headers, footers, exposed fitlers, etc. When you go to Content in the Panels / Page Manager interface, you'll find a 'Views Context' vertical tab with various bits of your view in it. This is the "bit more complexed" bit the guy refers to. If you want, you can go nuts and build a complex, sophisticated grid display placing the Views Row content type lots of times with different limits and offsets, with the first row highlighted, then a column showing rows 2-5, then a column showing rows 6-10... Or you can just stick the 'Views row' content in without limits or offsets (plus Views Header and Views Footer if you're using them) and it'll work as normal.
Place the Facets, Current View block, etc. This is the important bit for the question. Because the View is loaded at the start of rendering the page, the search is loaded at the start of rendering the page, so order doesn't matter. If it was a Views block, it wouldn't be done until that block was rendered. So your facets and current search blocks can go anywhere.


All of this is a bit rough around the edges and might not work first time. If you're using Search API Spellcheck, don't forget to put it in the View Header then place the View Header in Panels / Page Manager. If your view gets its search terms using Contextual Filters instead of Exposed Filters, sometimes it just works, but you might sometimes need to set the argument manually and occassionally check and patch supplementary modules like Current Search Links and Search API Spellcheck depending on how the search is set up.