Android App beta/alpha test apk not installing

Android App beta/alpha test apk not installing

My company has an app published in the google play store/android
marketplace. One of the issues that we're fixing in the next version of
the app is adding back xlargeScreen = true (it was somehow set to false in
the previous version, so now the app isn't showing up on larger tablets).
We're trying to get the alpha/beta testing setup so we can make sure we
have all our problems fixed before we push the apk to live.
I've uploaded an apk to alpha and published it. I made a google+
community, added it to the accepted testers and sent out the link for the
app. But, when we go out to the link and get set as testers nothing
happens. If I go to the google play store, it shows the date for the
newest upload to the account but the 'install' button attempts to install
the previous live version (which is incompatible with the test device,
yay!). Also someone else used their device and all the install did was
install the old version to their device.
I've considered the "wait up to 24 hours for the publish to go through"
being the problem, but the first alpha was uploaded Friday at lunch and
would not work at lunch today, on Monday. I moved the old apk to beta and
put a new one in alpha (more bug fixes yay) at lunch today. I checked all
the settings and everything looks correct, but I can't see how I'm suppose
to actually download the beta or the alpha at this point. And if I'm
suppose to download the production version 1) How am I suppose to do that
on the device that's incompatible with the production version and 2) how
do I choose between the beta and the alpha version?