How can you configure the first leg of RingOut call to ring both Desk phone and Softphone?

Can you clarify how you call RingOut in this case? What numbers you are specifying as "from" and "to"?

If you go to service.ringcentral.com, do you see that "DirectNumber" is assigned to your desk phone? In this case such behavior is expected. For direct numbers with attached line (device), RingOut routes the call directly to this device (all rules are bypassed). And, you are right, this behavior differs from regular incoming call where call passes through all defined rules.

If you want all your phones to ring in case of RingOut, you should specify direct number not assigned to any device or company number + extension (like +18001234567*102). 

But keep in mind, that there is one disadvantage of such approach: your second leg will start connecting before you actually pick up the first leg (internally call is answered by answering machine which plays announcements, starts finding you according to defined rules, etc). So the use you are calling to might pick up call earlier than you and hear your automated greetings. 

Can you  tell me your production phone number you specify as "from" for RingOut?

So, didn't it work as I described when you used +18885225975*126?

Actually there is one more way which is available for you in Sandbox and probably will be available in Production next week.

You can retrieve the list of forwarding numbers configured for extension using /account/~/extension/~/forwarding-number. In this list you will see the numbers of devices + external PSTN numbers available for call forwarding. You should be able to see your softphone in this list. Each of these numbers has ID. 

Now, when you call RingOut, instead of specifying  "from": { "phoneNumber": "XXXX"} you can specify "from": { "forwardingNumberId": "YYYY"} where YYYY is ID of your softphone.

It is new feature, and I wonder if it can be useful for you.

You can "fix" this behavior when calling +18885225975*126 by switching off all greetings/screening/etc. via Service Web. However I understand that it is not acceptable in general.

The approach with forwardingNumberId should work. The whole idea of RingOut was that if you want to use  your RingCentral number as "from", it should directly connect you to the particular desk- or softphone. Since we are hiding phone numbers assigned to softphones in some cases, the only reliable way is to select it by its id from forwarding numbers list. So, when end-user initiates RingOut call, he/she should be prompted to choose the endpoint (desk phone, softphone, PSTN number) where he/she want to pick up the first leg.