Apps for Outlook on Exchange 2013 only work in Safari on Mac OS X (not anywhere else)

Question

With Exchange 2013 SP1, a few "Apps for Outlook" are installed by default. I have not been able to get any of them to actually work... UNLESS I log into OWA from Apple's Safari web browser on Mac OS X. Safari on Windows loads the "lite"
Outlook Web App which doesn't load "Apps for Outlook" at all.
OWA on Internet Explorer 11 lists the apps within the emails, but they don't work (see screenshot).  The full Outlook 2013 desktop program lists the apps as well, but again they don't work at all. 
Am I missing some sort of configuration on Exchange 2013 that gets these to work on Microsoft's web browser and email client products?  It's kind of strange that they work on Apple's products so easily.  I've tried Chrome and Firefox on Windows
as well, but those don't work either.

Answer 1

Ah, okay. From the Exchange Management Shell, I did "Get-ECPVirtualDirectory | FL"
AdminEnabled                    : True
OwaOptionsEnabled               : True
Name                            : ecp (Default Web Site)
InternalAuthenticationMethods   : {Basic, Fba}
BasicAuthentication             : True
WindowsAuthentication           : False
DigestAuthentication            : False
FormsAuthentication             : True
LiveIdAuthentication            : False
AdfsAuthentication              : False
OAuthAuthentication             : False
DefaultDomain                   :
GzipLevel                       : Low
WebSite                         : Default Web Site
DisplayName                     : ecp
Path                            : C:\Program Files\Microsoft\Exchange Server\V15\FrontEnd\HttpProxy\ecp
ExtendedProtectionTokenChecking : None
ExtendedProtectionFlags         : {}
ExtendedProtectionSPNList       : {}
AdminDisplayVersion             : Version 15.0 (Build 847.32)
ExternalAuthenticationMethods   : {Fba}
AdminDisplayName                :
ExchangeVersion                 : 0.10 (14.0.100.0)
All seems to be configured as you say.  I didn't change anything, but realized the ExternalURL was pointing to DOMAIN.com/ecp which had a DNS issue, where-as
www.DOMAIN.com and mail.DOMAIN.com were all working.  So,
www.DOMAIN.com/owa was working fine on everything (except the Outlook Apps on Windows PCs), but DOMAIN.com/owa was not.  Now that DOMAIN.com/owa is working correctly, it seems that Outlook Apps are working correctly
too.  I guess even though we are accessing everything via
www.DOMAIN.com or mail.DOMAIN.com, the Outlook/Exchange Apps are still accessing stuff via
http://DOMAIN.com instead (unless the client is using Mac OS X Safari).  That sounds like that should be a bug in the way the Outlook Apps are loaded, no?