I don’t believe that this is a completely automated process. In other words, I think there is someone in Google looking at screen shots from your app making a qualitative judgement (probably an intern). This is my reasoning for arriving at that conclusion:
I have three versions of my app (Irish, UK and USA). They are basically the same with different text. The Irish version was released first and initially I encountered that message. I had implemented the manifest (like yours) and had one or two xml files in layout-sw600dp and layout-sw600dp-land and I couldn’t see the cause of the problem. I uploaded a new apk with new screen shots (no xml or manifest changes) and the problem went away. Here is the current status of the Irish app:
Next I implemented the UK version. It displayed “when you did it” as 12th June, the date the APK was uploaded. So at least there is a semblance of consistency in the review process.
Finally – the US version. To reiterate, this is basically the same app with the same xml as the Irish and UK versions and this is my current message:
Now it is quite possible that Google have written some code to look for xmls for large tablets. But if they had, I think my other APKs would be showing that error as well. Therefore, I think that the review process is partly manual.
So my conclusion – a quantitative approach may help (a few more xmls in sw600dp and sw720dp) but don’t neglect the qualitative stuff (choose screen shots that don’t display empty space !).
Update: re. the “Designed for Phones” message – December 2013
Since I wrote the above Google have introduced the dreaded “Designed for Phones” tagline and “Design your app for tablets” optimisation tips. This appears to be largely based on an automated scan of the apk when you upload it (probably the xml), so the process now seems to be more automated than was previously the case. Here are some points I have discovered which may help others:
1) I was unhappy that Google had designated one of my apps as “designed for phones” and I emailed them and they then removed this designation.
2) On a different app, I was getting the “design your app for 7″ tablets” optimisation tip. I added one fragment to my tablet xml in sw600dp like this:
<FrameLayout android:id="@+id/SideTab1" android:name="SideTab1" android:layout_width="300dp" android:layout_height="fill_parent" android:layout_marginLeft="20dp" />
and this did not remove the optimisation tip.
3)However when I made the same change to a second xml in sw600dp then the “design your app for 7″ tablets” optimisation tip was replaced by “Your layout should make use of the available space on 10-inch tablets”. More importantly, the “designed for phones” designation has now disappeared.
4) Obviously my next step is to make similiar changes in sw720dp.
Things seem to have changed again now (e.g. Google seem to now have removed the “designed for phones” designation in the country in which I am currently residing, and they seem to have relaxed some of their “rules” regarding the “design your app for tablets” message). Apparently, I am now doing “pretty well”, which is reassuring news !